Another option is to replace the whole rear end with one from the auto
wreckers.  Might be cheaper than having the dealer fix the old one.

Of all the clunkers I have driven, I have never had a rear end fail, so I
suspect the odds of getting a good one from the wrecker on the first try are
pretty high, and swapping out the rear end seems to be an easy DIY task.

OK guys... My plan for now is as follows.

0. The noises that I have are of two distinct kinds, a whining noise
that appears when I ease the gas pedal, and grinding noise that I hear
at low speeds.

1. I received the adjuster lock tab replacement from the dealer.

2. I will take off the diff cover again, and will try to adjust the
adjuster lock to reduce backlash to spec, using a dial indicator to
measure backlash. I hope (and would like you to confirm) that I can do
it using a screwdriver through the access hole.

3. If I cannot get a screwdriver through the hole, I could pull the
axle, and make a tool that goes through the axle hole and turns the
adjuster. I would make it out of some materials, I have a welder. What
I will need to know is dimensions of the tool (ie where to place the
pins etc).

4. After I do that, I will drive around to verify that the whining
noise is gone. If not, I will take the truck to a dealer. I realize
that the grinding noise at low speeds may remain, could be due to
trashed bearings.

5. If the whining noise is gone, I will take the diff apart and
replace the bearings that may have caused the grinding noise. I am
not, yet, sure whether it is easy or not to put it back together
correctly.

Does this plan make sense?

i