I'll offer this (without warranty).
You could probably have the ring and carrier assembly out in about five minutes.
Mark the two caps to the corresponding sides of the case.
Remove the two side adjust locks.
Loosen the four carrier bolts and back off the adjusters a couple turns.
Remove the four carrier bolts and tap the caps off.
If the carrier assembly don't fall out you may need to pry it a bit.
The pinion will likely require a puller especially if it has a 29 spline yolk and it's been on there forever. (Yolks should be hammered on.)
Remove pinion nut and washer. (A yolk wrench comes in pretty handy here.)
Attach puller to yolk and pull off the pinion.
Once the yolk is off, thread the nut back on and you should be able to tap/smack the pinion back out off the outer bearing, remove the nut, and pull the pinion out.
Remove the pinion seal, outer bearing, and any shims.
Use a long drift and drive out the outer race forward from the rear of the case.
From the front of the case drive out the inner race.
Reattach the case caps.
Pack & ship.
