This is going to be long winded, but I figured I'd try to list all the details of the ring and pinion setup from day 1.
First, I tried to use the factory service tool, which I bought on ebay, to determine the shim thickness. Unfortunately, the result of this process was a shim thickness over 0.1 inches, which was unreasonable. So, while the tool was useful for installing the bearing cups, it did not work for determining the shim. This meant that I had to use trial and error, so I made some "checking" bearings so I didn't have to press bearings on and off every time. Since the production shim I removed measured .034 (despite being marked "32"), I decided to start with the closest shim from the Motive Gear rebuild kit I bought, which was also .034. Note, maybe I got an incorrect set of shims in the kit, but the kit only included .021, .0295, and .034 shims (multiples of each).
With a .034 shim, I got the following results:
At the time, I thought that looked decent, but, since this was my first time setting up a ring and pinion, I decided to try another shim.
With a .0295 shim, I got the following results:
I thought that this looked pretty similar to .034, but maybe slightly more centered between the heel and toe. Since I though both patterns looked decent, I decided to order Chrysler shims of similar size. The reason for this was that the Motive Gear shims went behind the rear bearing cone, but the Chrysler shim I originally removed was between the housing and rear bearing cup. I figured that this would be easier to change out if I made a mistake. (It is very difficult to get the rear bearing off of the pinion shaft.) So, I ordered Chrysler shims for a Dakota 8.25" axle.
The parts catalog shows that the shim is between the housing and bearing cup, however, Chrysler must have changed the shim location/design over the years, or the parts catalog has an error, because, when I received the shims, they were the same size as the Motive Gear ones, meaning that they went behind the rear bearing cone as well.
So, I chose a Chrysler shim that measured about .0325 and fully assembled the axle with new bearings, crush sleeve, etc.
To be continued...