Skid63. That's a horse of a different color. You have some good background and know gears, bearing, races, shims and preloads. I feel better.
For everyone less informed, this is brief and allows for existing mechanical skill and knowledge to know what I am talking about.
You will need to secure the carrier in a stout vice or holding fixture.
The carrier that holds the ring gear is spaced with shims on either side of the carrier. Once the bearing caps are removed, us a pry bar to persuade the carrier out of the housing. It has a preload and won't come out easily. Keep the shims in the same location for a good starting point. Once the carrier is out remove the yoke and drive the pinion gear to the interior of the case to remove it from the front/outer bearing. There is also a shim under the inner bearing on the pinion gear. Be careful not to damage or lose it when removing the bearing. If you are using the same ring and pinion use the same shims in the same locations as a starting point.
If you are using new ring an pinion gears, look for marking on the pinion for a + or - and a number. This is the difference from the base setting to the pinion gear installed. This means if the pinion has a -2 it is .002 less the base spec. The shim would be .002 different than the 0 point. 0 point of pinion depth is found with special tools. But if you track the shim from the old one, you can get by. Compare you new pinion to the old pinion and adjust the shim thickness based on the numbers. If there are no numbers assume 0. I said assume because sometimes the original number was painted instead of stamped, and is gone. If old and new are both 0, or both the same, use the original shim.
When removing the old bearings from the pinion gear, you will see a sleeve between the two bearing inner races. This a preload crush sleeve, and must be replace with a new one. When installing the pinion gear nut, you will set rotational preload in inch pounds. Check the specs. This will require a holding bar or fixture to hold the yoke/pinion gear still while tightening the pinion gear nut. If you overshoot replace the crush sleeve. Backing off won't do it.
The side shims on the carrier need to be redone when replacing the ring and pinion also. Set the carrier in place without the shims. Move the carrier so the ring gear sets at 0 tolerance to the pinion gear. Add shims to the left side (ring gear side) to maintain 0 tol. Now measure the clearance on the right side. Add shims to maintain 0 with not play in the carrier side to side. Now add .008 to the right side. This sets the carrier preload and move the ring away from the pinion to create some backlash. Check the spec for total backlash. Measure it by rotating the carrier with a dial indiator on ring gear tooth.
There is a spreader that can be used to spread the housing so you can drop the shims in place. There is also a curved driver to tap them in if the spreader is not available. You can use a soft punch. Just done mushroom the shim and mess up the parallel surface or the bearing will whine and wipe out.
Now use gear marking paint or paste and rotate the ring and pinion several turns. Rotate it in the direction of forward vehicle motion. You want the pattern to be centered on the face of the tooth. Valley to top, and toe to heel.
If the pattern is off you will need to adjust the shims. The pinion shim to adjusts depth. Thicker will run it to the Valley. OR you may need to change carrier side shims to change heel toe position. Be sure to add on one side and subtract the other side to maintain equal preload. There is some influence from any shim is multiple pattern direction, so it may not be simple, but not that bad either. Don't worry about coast side pattern until the drive side is correct. Then the coast side will be good or something is misaligned or bend.
With your knowledge I would recomment a tape from Richmond Gear. It shows ring and pinion install and set up. They used to and may still supply it with new gear sets. Good but not for rookies. It's too brief. There are also some decent books from Summit and Jegs.
I'm fairly sure you have or can get you hands on micrometers, feeler gauges, beam type inch pound torque wrench, foot pound torque wrench, gear mark compound, prybars, and holders to hang on to the pinion. With out the pinion depth measurement tools you may go through a few crush sleeves, but hopefully not more than one or two. You will need to know where you can locate the shims, if needed. It's not likely you will find a pinion depth gauge or case spreader, but you can still do the job.
It's early 
