Nice work!

I've got a kit like this to press bearings and bushings in.
ATPEAM 52-in-1Custom Bushing Driver Tool Set | Transmission Wheel Axle Bearing Race Seal Installer Remover | Bush Removal Puller Bearing Press Tool Kit https://a.co/d/5TgStxz

This is interesting, I've never come across lsd for e53 automatic. I've seen lots for manual tranny, but never automatic. Please take lots of pictures when installing.
My diff is out right now, I had it sandblasted and coated.

I would consider installing an lsd as well. Do you have a link for the bearing set?
Here in canads they don't sell any.
I'm rebuilding the transfer case, and purchased a bearing kit, but a couple of bearings were plain wrong. One of them didn't have a snap ring groove in, so I had to chase that bearing somewhere else.

I may follow your footsteps and do the differential.
The only reason I'm a bit apprehensive about the differential is the pre-load you're dealing with right now.
Did you install a new crush collar? For the life of me I cannot find one.
I heard if take of the collar but, you're supposed to replace the crush sleeve, or differential will fail a few months down the road.
Are you reusing the old one?