Forgot I was going to suggest something here.
Of course have both wheels off the ground. With the cover off, rotate the carrier around until you DON'T see all the junk in the pictures posted in this thread. You'll see the pinion shaft, maybe the ends of the axles, and the pinion gears.
Remove the pinion shaft lock bolt, which goes in from the passenger side of the carrier, parallel with the axleshaft. Goes right through the pinion shaft and carrier. On my 14SF socket needed was a 10MM, on the 10 bolt's I *think* early on were 5/16"...if GM was smart they went bigger on the 10 bolts later too. Anyways, remove the lock bolt, and hope it doesn't break. If it does, replace the axle.
Now if you DON'T pull the pinion shaft all the way out, but out of ONE pinion gear (thats their real name) and hold one wheel while rotating the other, I believe it will spin the pinion gear out into the open part of the carrier. I don't like pulling the pinion shaft completely unless you have to, as you start dealing with other issues.
While in there I would give the fine toothed gov-lock mechanism a THOROUGH going over...rotate the carrier watching all the gears, making sure teeth aren't broken. It takes the smallest piece getting into them to break.
You'll probably want to replace the pinion gear thrust washers at the same time.