Contemplating an adjustment of the ring and pinion gears can leave the average shadetree mechanic quivering. Just thinking about all those special procedures and tools mentioned in the manual will have you curled up in a fetal position and crying. I'm not ashamed to say I was in that club, I mean other than the crying thing. Nobody can prove that anyway. While it is time consuming and requires much patience, anybody with the right tools can do this project. HowStuffWorks.com has an excellent overview showing how a differential works.
Some of the procedures listed are what I devised while doing this project. Since accuracy is so important, I've included some extra steps that may add more time, but will hopefully let the average mechanic like myself have excellent results. If you find some of my steps different from the service manual, it is because I've tried to come up with procedures that require a minimum of expensive or hard-to-find tooling. I'd like to extend a big thanks to Ric Meagley Sr. for helping me with details of the shimming process.
Keep in mind you may not need to perform any maintenance inside the differential. With a good supply of oil available, the bearings and gears may be just fine the way they are. The outer bearings are more prone to abuse, as they support the vehicle weight and may not have seen any fresh lube since Disco somehow ruled the airwaves.
Keep track of the existing shims during the rebuild process. That is usually an excellent place to start the adjustment process. During a rebuild, don't just reinstall the shims as they were and hope everything will be okay. I'm pretty sure that is what happened to this axle after new bearings were installed, and some of the tolerances were way out. Even though new bearings and races will have the same dimensions as the old when they were first installed, there is no guarantee the last guy knew what he was doing. Components will wear and even distort slightly, meaning the original settings may no longer even be accurate. Take the time to double check all the various clearances. Mark all items, such as the ring gear's orientation to the carrier, to allow reinstallation exactly like it was before. As far as remembering which shims went where, here's a suggestion offered by one reader: "Take scrupulous notes as to which shims are located where with each trial fitting. Smudged notes, written in Sanskrit by the fingers of your non-dominant hand while the heel of said hand attempts to hold down a smudged Post-It page, do not fit the definition of scrupulous. Thank you for not asking me how I know this." (Normally all contributions are given due credit, but I think it would be best to keep this one anonymous to avoid embarassing Tom McClay.)
Most of the pictures below show the special stub shaft arrangement for my Vern-O-Lock locking differential. The procedures would be the same for the stock differential, too. The ring gear is not installed yet in some of these pictures.
Not all of the myriad tools mentioned in the manual are needed, so don't let that scare you. Lots of fancy jigs are mentioned for checking the mesh of the ring and pinion gears. That job can be done by using Prussian Blue marking dye. Resist the urge to scratch your nose while using Prussian Blue. Don't ask.

Right off the bat, the manual says you'll need a case spreader to remove the differential carrier from the axle housing. The cast iron axle housing has an opening slightly narrower than the differential carrier and its tapered roller bearings. This interference fit squeezes the bearings together to apply the proper preload. Per the manual, a case spreader is used to carefully stretch the housing for removing or installing the differential carrier. An alternate method was mentioned, using a pair of crowbars. This seemed horribly crude and I was very reluctant to try it. For giggles, I decided to give it a quick trial. Instead of the crowbars, I used two pieces of wood. I only had to apply the teensiest effort, and the differential carrier popped right out. Note the sockets for the case spreader:

For installation, the bearing races are started at a slight angle to make up for the interference fit. The angle is exaggerated in this picture. With just a couple of gentle love taps with a hammer and wooden block, the differential carrier dropped right back in. This method also worked fine on my '51 wagon's Model 44 rear axle:
Should you decide to use a case spreader, the manual lists some very important precautions. Release the pressure as soon as possible. Otherwise the housing may take a set in the expanded position and become worthless. Use of a dial indicator is mandatory to prevent spreading the case more than the maximum .020" specified, or once again the case could take a set. Here is a scan from the manual showing a case spreader in use. If you look closely, this is a picture of a Model 44 axle, which has a different shaped cover:

After the installation is complete, the races for the carrier bearings are held in place by the bearing caps. This picture shows how the bolt holes extend through the axle housing. Apply sealant to prevent gear oil from leaking out the front via the threads. To seat the bearing caps properly, tap them gently with a mallet while torquing the bolts. Of the four bolt holes, only three extend to the outside and need sealer. I applied sealer to all four bolts so there would be no difference when torquing them down:
Treat these caps just like rod or main bearing caps on an engine crankshaft. Mark the caps before removal so they can be reinstalled exactly as before. There is no guarantee that the bearing caps were previously installed correctly. While the carrier is removed, reinstall the caps for a test fit and make sure the inner edges of the caps match up with the main housing.
The bearing cap bolts are under a lot of stress. Inspect them carefully for any signs of elongation. If you can't reach final torque during installation, that is because the bolts are stretching. Stretching will occur in the section next to the unthreaded shank. In this image, the reduced diameter from stretching is being measured. Compare that reading with the undamaged section at the tip of the bolt. One of the bolts had a .010" difference. I don't know what a normal limit would be, but that seemed like a lot. All four bolts were replaced:

Before starting the adjustment of the ring and pinion gears, set the clearance for the spider and side gears inside the differential carrier. The clearance is adjusted by use of shim washers. Should any of these gears need to be replaced, they should be replaced as a set of four. Due to the ring gear's thickness, it will have to be removed to pull out the shaft for the spider gears. You could check the clearance with the ring gear installed, but it would have to be pulled for any shimming of these four gears. Here is a backside view of the gears and their shims. Note the cupped washers for the spider gears:
Here is the differential carrier and roller bearings, less ring gear. This shows where the spider and side gears fit inside. Note the concave surface for the spider gears:
In this picture, the side gears are already installed and the spider gears are being held in place. While holding the spider gears, all four gears are rotated as a unit so the spider gears fit inside the carrier:
Once everything is in its place, wiggle the gears and tap the unit on the bench to ensure full engagement. Using a pair of feeler gauges, measure the clearance. It is important to use two feeler gauges, otherwise the side gear could tip slightly and give an inaccurate reading. I would also suggest rotating the gears when checking this clearance, as explained in the next paragraph:

While checking the side gear clearance as shown above, I found the gap excessive. After much searching, I was able to find some thicker shims for the side gears. Only after installing them did I discover a curious wear pattern in the gear teeth. When the gears were rotated, the gear teeth did not mesh as tightly as in the fully seated position. This caused binding using my new, thicker shims. I had to remove them, and reinstall the standard thickness shims. Only then was I able to have no binding when rotating the gears. This left my clearance slightly over when the gear teeth had the maximum mesh but I don't think this will be a huge problem. My only other choice was to replace the set of gears but I did not think that was needed. This problem with the shims was not a big deal, except I did not discover it until everything was reassembled. If the gears are rotated while checking the side clearance, you may hopefully avoid this problem.
There is one other word of caution about these shims. I replaced the cupped washers for the spider gears, but the curve was not a perfect match. This lack of conformity was enough to raise the spider gears from their seats by several thousandths of an inch. This would give a misleading reading when the side gear clearance is set. But once the axle is driven under load, the new cupped washers would quickly conform to the curvature and result in excessive clearance. My old cupped washers had minimal wear, so I decided to reuse them. Unless you find lots of wear, I'd suggest reusing them for this reason.
Although I left it out for the Vern-O-Lock, don't forget the spacer between the axleshafts for the stock semi-floater. After everything is properly assembled, install the lockpin to hold the pinion shaft in place. The lockpin needs to be peened in place at both ends. You could use a hammer and center punch, or an air hammer as shown:
It is time to bolt the ring gear back in place. Make sure the mating surfaces are clean and free of burrs to ensure the ring gear runs true. I took a belt & suspenders approach, and used both the strap locks and Loctite. Not many people know this, but besides locking threads, Loctite makes a great desert topping:
It is uber important that the ring gear bolts be torqued evenly to prevent warpage. Use a cross pattern like when torquing lug nuts. Work up to the final torque in several stages:
If you don't have a torque wrench yet, here is another accurate method to set the torque using a hammer. It takes a bit longer, but if done correctly, the end results are the same. If left-handed, click here. If right-handed, click here.
When bolts get easier to turn, that is never a good thing. Like with the differential bearing cap bolts, I found three of these ten bolts could not reach final torque. The torque is quite substantial, and the bolt necks stretched. When I looked at the other side, the stretched bolts had a few extra threads showing. I'm using calipers to check the difference in this picture, but it was apparent to the naked eye. All ten bolts will be replaced:

The stock bolts are real oddballs. They are 3/8-24 x 1.125", a standard size, but the heads are 11/16". (A standard 3/8" bolt has a 9/16" head) My local 4WD shop tried to sell me that the shorter (3/4") bolts for a Model 44 axle, insisting they would be just fine. A trip to an industrial supply house netted some 3/8" bolts that would work. The length of the unthreaded shank next to the head needed to match. Bolts that have threads all the way up to the head aren't suitable for shear-loaded applications like this. For maximum shear resistance, the ring gear needs to be in contact with the solid shanks, not threads. I had to buy 1.375" long bolts and cut off the extra length of threads. These bolts had a standard 9/16" head, so I bought some hardened washers to spread the clamping force just like the larger 11/16" heads. Don't buy run of the mill washers. They need to be hardened or they will distort under load and the bolts will lose their clamping force.
The rest of this section deals with shimming the ring and pinion gears for a satisfactory mesh. Keep in mind that shimming affects not only gear mesh, but also bearing preload. In addition, it is very important that the ring and pinion gears be kept as a matched set, whether new or used.
If replacing the bearings, a good suggestion is to take the old ones and oversize the bores. A brake cylinder hone can be used as shown, but be aware it is a very slow process. New slip-fit bearings can be purchased from automotive specialty shops, or a machine shop can perform the modifications for you. Slip-fit bearings will slide on and off quickly. The aft pinion bearing, closest to the gear teeth, doesn't need to be bored out because the new bearing will not be removed from the shaft during the adjustment procedure. :

Keep in mind that the combined thickness (stack height) of a used bearing and race might be slightly less than a new set due to wear. With calipers or a micrometer, compare the stack heights of the new and used sets. If different, make a note so you can adjust the shim packs accordingly during final assembly. (New slip-fit bearings will be the same as new press-fit bearings.) The following illustration shows how the stack height would decrease due to wear on the rollers and mating surface on each race:
Some of the following steps cover how to pull the new bearings into place, which will not be applicable with the oversized bearings. If replacing the bearings, replace the races as a matched set, too
When removing the bearings, expect to bend or kink a shim or two. They will pull down flat when installed so there is no problem to reuse them unless they are severely damaged or are folded back on themselves. If you hold the shims together and measure the total thickness, you will get an exaggerated reading due to the gaps. I highly suggest measuring a flat spot on each shim individually. Label each shim with a Sharpie magic marker. If, for example, you wanted a stack of shims totaling .024", you'd know to use a single .004" and two .010" shims. Otherwise, you might stack two .010" shims and mistakenly read .024". I don't think we need to discuss how I know this.

Here we see the carrier bearings being removed with a bolt-grip puller and bearing splitter. (These two pictures were taken before I reinstalled the ring gear.) One of the mandrels from the driver set is being used to bridge the hollow end of the carrier. Make sure the bearing splitter grabs the center section of the bearing instead of its rotating cage:
The bearing in the previous picture was easy to grip. It was very difficult to get the bearing splitter under the opposite bearing. I had to grind down the splitter for clearance. Although a splitter is the preferred method, another option is to use the notches cast into the carrier. If you look carefully, this is the carrier from the Model 25 front axle, which had even less clearance for the splitter:


I couldn't find any sort of puller with jaws deep enough to fit around the bearing and into the notches. A rolling head pry bar can be used. It must be narrow enough to fit in the notch. Like with the bearing splitter, make sure you apply pressure to the center race and not the rotating cage of the bearing. With the carrier held in a padded vise, pull on the pry bar while tapping with a hammer. The jarring action from the hammer will lift the bearing slightly. It will be necessary to work from opposing sides a little bit at a time. The pry bar might leave small burrs at the notches, so make sure you clean them up for accurate shimming:
This exploded view shows the shims behind each of the carrier's tapered roller bearings. The combined thickness of the shims on both sides controls the preload on the bearings. To adjust the mesh of the ring gear, move the shims from one side to the other, keeping the same total amount of shims for a constant preload:

In this image, a stack of feeler gauges is being used to determine carrier bearing preload. With no shims behind the bearings, force the carrier as far as it will go away from the pinion gear and measure the gap. If you pushed in the other direction, the pinion gear would limit the travel and the total gap would have to added up from each side. Use a pair of gauges as shown to keep the bearing cup even. Unless you have an extra thick set of feeler gauges, you'll have to stack several blades together. To this gap, add the amount for the bearing preload, .015" for the Model 41 and 44 axle. Select a stack of shims for this new total. Divide this into two stacks, with one about .010" thicker. Install the thicker stack on the side facing the ring gear teeth (to the right in this picture) and reinstall the bearings. It is important to understand this only sets the bearing preload, and does not accurately adjust the gear mesh. The purpose of the thicker stack is to keep the ring gear from being too tight against the pinion gear for our initial setup. In later steps, we'll redistribute the shims to fine tune the gear mesh. If keeping the existing shim packs, make sure the combined thickness includes the extra .015" for preload. Note the new ring gear bolts with smaller heads. This precluded the use of the strap locks, but Loctite will still do the job:

My method to set the carrier bearing preload is different than what is in the manual. The manual calls for some complicated, unobtainable tooling to preset the pinion gear depth for proper meshing with the ring gear. (Pinion gear depth is a fancy term for fore/aft placement of the pinion gear shaft) Then the manual has you set the carrier bearing preload by pushing the ring gear against the pinion gear, and adding a certain amount of shims to each side. That would have given a proper preload and a reasonably accurate mesh right away. Since we don't have that fancy tooling, we can't accurately determine what shims to initially add to each side of the carrier. The preload will still be accurate, and we can go back and fine tune the mesh after the pinion gear shaft is squared away. Even if using the tooling to preset the pinion gear depth, minor changes to this adjustment are made later as needed for the proper gear mesh pattern. While this tooling would be beneficial in a production setting, entirely accurate results can be obtained simply by observing the gear mesh pattern.

Although the Model 41 and 44 axles are similar, the arrangement for the pinion gear is different. There is a collar and shims between the bearings for the pinion gear shaft. This is a rigid collar, not a crush sleeve like in many other brands of axles. Unless you have an original CJ-2A service manual, the later, more common manual only shows the Model 44 axle which does not have the sleeve. The Model 44 has a shoulder on the pinion gear shaft for the shims to bear on, much like the spacer on the Model 41. Here is a scan of the Model 41 rear axle cross section, from a 1948 owner's manual:

Pulling the pinion gear shaft is not easy. Just loosening the big nut inside the U-joint yoke can be an ordeal without the right tools. It is torqued in place with 220 ft-lbs. With a big impact gun, it will pop right off and there is no need to even hold the yoke still. Without that, you are left to find some means to break that nut loose while holding the yoke. My homemade yoke holder can be seen in the Tool section. The manual shows a special wrench with a rectangular opening to fit around the outside of the yoke. Some folks have had success holding the yoke with a big monkey wrench and some padding. Even though I had the nut loose, I decided to try this as a ControlledScientificExperiment(tm). It was pretty difficult to hold the yoke this way. If you looked at the wrench sideways, it would slip off and mar the yoke. I would not recommend using a monkey wrench like this:

Once the nut is loose, you didn't think that yoke would slip off all by itself, did you? Time for the trusty bolt-grip puller. Two bolts are fitted to the U-bolt holes on opposite corners of the yoke:


Here is what the backside of the yoke looks like. Note the surface that rides inside the oil seal. Don't be surprised to find it scored or otherwise damaged. It can be turned down slightly on a lathe and the seal will adjust. A Speedi-Sleeve repair can also be used. The yoke includes a shield to help protect the oil seal from debris. On the rear axle, the shield extends beyond the edge of the axlehousing casting to deflect debris. On the front axle, the shield is smaller since a larger one would catch debris while moving forward. Ensure that the shield is securely swaged on the yoke. This shield worked loose on me and made an intermittent ringing/grinding racket that was difficult to track down. When the yoke is reinstalled, add a smidge of sealer at the end of the splines. This stops oil from migrating along the splines and leaking out around the nut.:

Considerable force is needed to drive the pinion gear shaft from the housing. In this picture, I'm using an air hammer with a brass faced punch. Lacking that, a heavy brass drift and big hammer will be needed. You could also leave the yoke installed and drive the shaft out from the yoke and housing at the same time:
With the pinion gear shaft out, pull the front oil seal. Use a hook type seal puller as shown, or reach inside with a locking jaw slide hammer:
Take a look inside the housing. This view is from the front, showing the bearing cups still installed. The manual shows a fancy puller to remove these bearing cups. There are notches inside for a brass drift, so that puller is not needed. Note the passage allowing oil to reach the front bearing :
Here is a view of the bearing cups from the aft side. There are shims, not visible, between the aft bearing cup and the housing. These shims control the pinion gear depth, or how the pinion gear meshes with the ring gear. There are no shims at all on the front bearing cup. When you use a brass drift to drive out the rear bearing cup, it might damage the shims. Ripples or dents in the shims are no problem and will be flattened when reinstalled. Watch out for rips or tears that could get folded over and change the settings:

Through the power of positive thinking, I was able to get all the components of the pinion gear shaft to stand up nicely for an exploded view. Bearing preload (not pinion depth) is adjusted by shims against the spacer. The aft bearing would not have to be removed from the shaft for any adjustments, unlike other model axles. If you do need to replace the aft bearing, it is an interference fit. Stick the pinion gear shaft in the freezer when your wife isn't home. Cover it (the shaft, not the freezer) with a light coat of oil to prevent rust from condensation. Heat up the bearing. A Ziplock bag in warm water works well. Press the bearing in place quickly before the temperatures equalize:

The adjustment of the pinion gear shaft is done in two distinct stages. Pinion depth (the mesh adjustment) and bearing preload are separate. First, pinion depth will be adjusted by the shims at the aft bearing cup. (Remember, pinion depth is just a $10 word for the fore/aft placement of the pinion gear shaft.) Then the bearing preload is adjusted by the shims against the spacer (or shoulder on the Model 44).
Before we get into shimming the pinion gear, it is very important thing to check the runout of the ring gear. I'm mentioning it now, because it is easier to check with the pinion gear shaft out of the way. It can be done with the pinion gear installed, but you'll have to spin the pinion gear shaft to turn the ring gear. Here you can see a dial indicator checking the runout on the face of the ring gear. The tip on the dial indicator is wide enough to keep from falling between the teeth:

Although not shown, I also checked the runout on the backside of the ring gear. There is no guarantee the ring gear thickness is constant. I'm placing a lot of emphasis on checking the ring gear runout. Since the gear mesh is partially determined by the side-to-side placement of the ring gear, excessive runout will give uneven results. There is no way to correct the runout other than replacing the carrier or trimming the mating surface with a lathe. (My lathe wasn't big enough or I'd have done this.) However, by cleaning up a few burrs, I was able to cut the runout in half and bring it well within tolerances.
When you start fine tuning the gear mesh, even this runout within specs will still give trouble. A perfect mesh at one spot on the ring gear might be way out at another due to the runout. Use the trusty dial indicator to find the middle range of the runout and mark it. Use this spot for checking the mesh and any potential difference around the ring gear will be cut in half. I originally started checking the mesh without finding the middle of the runout range. After making some adjustments, I checked again but didn't keep the same spot on the ring gear. What should have been a fine adjustment appeared to make a big change and I was baffled. When I made a big adjustment to compensate, it barely showed up. I was confused until determining the difference in runout was the cause.
If installing a used ring and pinion gear set, use the carrier from the donor axle if at all possible. The ring gear teeth would have worn to match the carrier's runout. The end result, irregardless of the carrier runout, is that the ring gear teeth would be more or less even from the perspective of the pinion gear. If a ring gear and carrier cannot be kept together as a matched set, determine the high and low spots of runout for each carrier and mark the ring gear. Reinstall the ring gear on the other carrier accordingly and the runout on the face of the gear teeth will be kept to a minimum.
With the ring gear marked for runout, let's move on to shimming the pinion gear shaft. We will initially set the pinion gear depth, and then come back to set the preload later. Make sure you have an appropriate amount of pinion depth shims at the rear bearing cup. The existing shim pack is a good amount with which to start. This image shows a bearing driver being used to insert the rear bearing cup. There is no need to go overboard with the hammer. When the pinion gear shaft is tightened in place, it will pull the cup and shims tight against the housing.:

Leave out the preload shims (on the shaft) for the initial checking of the gear mesh. The forward bearing is an interference fit and is tough to get on the shaft. A third hand is helpful to hold the pinion gear shaft in place while tapping the forward bearing onto the shaft. There is no need to install the oil slinger yet, just forward of the bearing. Nor should you install the oil seal until all adjustments are done. I had to start the nut without its washer so I could catch a couple of threads and start pulling the bearing and yoke into place on its splines. Once started, undo the nut and add the washer.
To save the extra work of pulling and installing the yoke for each adjustment, you could make a spacer to take the place of the yoke. 1.230" minimum inside diameter and 1.375" long would slip right over the splines. That is slightly shorter than the yoke to make it easier to get the nut started. A stack of big washers would work, too, as long as the outside diameter didn't hit the housing.
This axle had a cotter pin and castellated nut on the pinion gear shaft. Some axles may not have provisions for a cotter pin. A self-locking nut is used instead. Because this nut may need to be removed and installed several times, use an ordinary free-running nut during the adjustment procedures to limit wear and tear on the shaft threads. For final assembly, install a new self-locking nut. Do not reuse the old self-locking nut as it may not have sufficient grip anymore.
This is where the fun starts, as you will have to apply a lot of torque to pull the bearing onto the shaft. (Heating the bearing and cooling the shaft will help) An impact gun won't work here by itself, as it will just try to spin the yoke. I used my yoke holder. Another untested idea is to install the ring gear and jam a piece of wood in between the gears to stop the rotation. Since the preload shims are not installed yet, don't just torque the snot out of that nut. Torque it only enough to give the specified rotating drag on the pinion gear shaft. The rotating drag should fall in the range of 10-25 in-lbs (not ft-lbs), covered in the next paragraph. I found that by seating the nut with 95 ft-lbs, the rotating drag came out pretty close. After torquing that nut, tap on the inside end of the pinion gear shaft with a brass drift and hammer. Retorque, then double check the rotating drag. This will ensure that the aft bearing cup and shims are fully seated in the axlehousing. I had to do this torque, tap and recheck procedure three times to fully seat the aft bearing cup and shims. I knew it was fully seated when the rotating drag didn't decrease after tapping on the pinion gear shaft.

For reference, an average person can apply a maximum of approximately 25 in-lbs holding a screwdriver with one hand. I did a few calculations (Hats off to math teachers everywhere) and figured how much force to apply to a breaker bar using a fish scale. Keep the breaker bar near vertical so its weight doesn't affect the delicate readings. Hold the fish scale at a right angle to the breaker bar.
Here is the formula to calculate how much force to apply for a certain torque value:
T (in-lbs) = L (handle length in inches) x F (force in lbs)
When I could pull the breaker bar with a force anywhere from 0.6 to 1.4 lbs, I knew the preload was correct. Those numbers are only correct for the 17.5" breaker bar handle I was using. Apply the formula using the length of your breaker bar handle. The 17.5" measurement was to a hole where I hooked the fish scale, not to the end of the handle. I'm using a 0-10lb scale in the picture, but a lower range scale would make it easier to determine the required amounts:
Update: I recently picked up a nice inch-lb. torque wrench. The dial has a follower needle to show the maximum value obtained. While this torque wrench is easier to use, it is no more accurate than the breaker bar and fishing scale method:
Now is the moment we've all been waiting for, checking the gear mesh. Brush some Prussian Blue dye on the ring gear teeth and torque the caps in place to secure the differential carrier. Rotate the pinion gear shaft and observe the pattern where the pinion gear wipes away the dye. Remember to base all subsequent adjustments on a spot in the middle of the ring gear runout like previously mentioned.
Here is a scan from a 1954 Motor Service Automotive Encyclopedia. This is a nice illustration showing which way to shim the gears for a perfect mesh. Remember that the pinion gear depth is controlled by the shims under the rear bearing cup. Side to side placement of the ring gear is controlled by moving shims from one side to the other on the differential carrier:
Note how that scan made mention of the drive and coast sides of the gear teeth. This image shows which side is which for a rear axle It may not be possible to get the mesh perfect on both sides. In that case, set the drive side for the best mesh possible while making sure the coast side is not too far off. It may be necessary to use a compromise setting. Favor the drive side since that is where the all the high speed use will be, unless you learned to drive by watching the Rockford Files:

The actual process of reading the gear mesh with Prussian Blue dye is somewhat anti-climatic. Give yourself plenty of time to go through each round of adjustments, and take plenty of breaks. Reapply fresh Prussian Blue on the ring gear between adjustments so that you don't mistakenly read the old marks. Taking the ring gear runout into consideration, make sure the mesh is not too tight at any one section. As previously mentioned, the ring gear teeth have probably worn into a somewhat even pattern from the perspective of the pinion gear, even though the carrier's mounting surface has some runout. Also make sure that the rotating drag of the pinion gear shaft is consistent for each check.

With the gear mesh satisfactory, a check of the gear backlash is next. In this picture, the dial indicator has an extended rod to contact one of the ring gear teeth. Keep the pinion gear shaft stationary, and see how much the ring gear can be rotated. Check once with the ring gear's area of greatest runout meshed with the pinion gear shaft. This will produce a tight backlash reading. Then check again with the area of least runout, which will show the area of greatest backlash. The specified range is .005" - .010". If the backlash is too great, the ring gear and pinion gear shaft must be shimmed closer to each other. If the backlash is too tight, move the two gears apart. In either circumstance, aim for the best compromise gear mesh pattern that puts the backlash within specifications:


All that is left is to set the preload on the pinion gear shaft. This is controlled by finally adding the preload shims on the shaft. A .065" thick stack of preload shims is a good starting point. Remember in a previous step where the rotating drag was set to 10-25 in-lbs? That will need to be duplicated, only this time with the nut fully torqued to 220 ft-lbs and with the preload shims installed. The purpose of the shims is to limit the travel of the two bearings towards each other.
If you've happened upon this guide and are using it for a different axle with a crush sleeve, there is something you must understand. The purpose of a crush sleeve seems a bit mystifying. It is merely for faster setting of the pinion gear shaft's bearing preload. The use of individual shims is time consuming while setting the rotating drag during final assembly. Remember the preload shims limit the travel of the two bearings towards each other when the nut is torqued. A crush sleeve performs the same function. The crush sleeve collapses a carefully designed amount as the nut is tightened. The collapsed crush sleeve then maintains that same dimension, just like a rigid spacer and shims. The use of crush sleeves saves a lot of time during assembly in a production setting. It is important to realize that a crush sleeve does NOT act like a spring and must be replaced during a rebuild.
It takes a lot of heft to apply 220 ft-lbs on the nut. Luckily, all those years of little chocolate donuts paid off for me. You will need to use the yoke holder again while applying torque. With the nut torqued properly, measure the rotating drag again. Add or remove preload shims so the rotating drag is within specs with the nut torqued to 220 ft-lbs. Remember that the pinion gear depth has already been set, so the shims under the aft bearing cup won't be touched during this step. You will have to remove the differential carrier one last time for checking the rotating drag.
Because the carrier roller bearings sit up fairly high relative to the oil level, they should be prelubricated with grease during final assembly. The grease will provide lubrication during initial break-in and then slowly dissolve into the gear oil. The pinion gear shaft bearings will be submerged so their prelubrication is not essential.
If desired, you could work on the bearing preload while also adjusting the pinion gear shaft depth. I've listed the preload adjustments near the end to avoid confusion. If you feel comfortable enough making two adjustments at once, you could save some time. Setting the pinion gear shaft preload is a very delicate operation and a minor change in shim thickness will make a big difference, so proceed carefully. By this point, you may have removed and reinstalled everything a few times, so don't let frustration set in.
Once the preload shims are correct, remove the yoke again. Install the oil slinger on the shaft. To install the oil seal, a special driver will be handy. This next picture is a profile of the oil seal, showing how it does not have a flat exterior surface:
A plastic pipe fitting with a 3" outside diameter worked perfectly. It fit right down in the channel of the oil seal. The hollow center cleared the protruding shaft. Work carefully around the circumference so the seal goes in straight. The seal will fit slightly below flush with the housing, so some type of seal driver will be needed:
Lubricate the lip inside the seal and reinstall the yoke, washer and nut. Orient the shaft so the cotter pin can be easily installed from the open sides of the yoke. Don't forget a smidge of sealer on the ends of the splines. Torque the nut to 220 ft-lbs one last time and install the cotter pin. The rotating drag on the pinion gear shaft will increase with the seal in place, so don't let that alarm you. Reinstall the carrier and torque the caps in place. Don't forget the sealer on those bolts.
Make one last check to ensure the mesh has not changed, and you are done. This may all sound like a lot of work, but it is not horrific. I took a lot of extra steps taking pictures and got good at pulling the carrier and pinion gear shaft. With a little practice, I could pull, reshim and reinstall everything in about fifteen minutes. With the right tools and enough coffee, you could have similar results.
For one last thing, check the U-joint yoke for gouges. Mine had plenty from past encounters with a monkey wrench. To prevent cracks from forming, take a few minutes to blend out any sharp edges using a die grinder.