My rear diff whines as well. X5 2002 3.0
I was wondering what that loud whine was, it scared me. Very similar to "alternator whine" that I once had with a new audio system..
I figure it must be the diff, unless I did something wrong with the transfer case rebuild. However I was pretty confident with the transfer case job, not so much with the diff 4.10.
On top of adding the LSD locking plate from racingdiff, I also used 2 diffs to make one lol! And never checked the gear teeth pattern. So who knows, maybe the diff will die soon. The whine comes and goes, but it's there on acceleration, not just coasting. Not sure if the rear diff goes, can it damage the transfer case.

In terms of NV125, I did a full rebuild, chain, all bearings and seals. I'll be posting a video in a couple of weeks, it's pretty long and it going through editing now. Hopefully it will be helpful to whoever wants to rebuild their TC.