Rear end noise
If you mean shim the carrier I suppose this could be possible but you need to know for sure what the specs are before you start messing with it. Check it with a dial indicator for the backlash. You should be able to see on the face of the ring the desired B/L scribed in although if factory gears this is not always the case. Look for sonething around 8 to 12 thousands.
Pinion depth
This will also affect you backlash. When setting up gears you always start here first and everything else is shimmed off of this.
Yes the usually involves pressing on and off a pinion bearing with a new crush sleeve or desired pinion spacer.
Worn gears
Finally if you were able to make all of the correct adjustment with the pinion depth and carrier backlash and had be best looking pattern in the history of patterns it still may whine because the gears have already been worn in a crtain pattern together.
Summery
I bought my car with 4.10's that sounded pretty rough. With unknown mileage on them I opted to just put in a new set with all new bearings. I know it is new and done right.
If your set is factory you can usually get by with reusing the same shim on the pinion as a great starting point. I didn't have a pinion shim on my hacked up job so I had to start from scratch. I made a test pinion bearing out of the old one. I ground it out a little so it would just slip on and off the pinion for measuring purposes
Yes I did check the b/l on the old set before I removed them. I believe it was around 36 thousands. Oh yea well worn.
Good luck.
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