Long story short, I need to transplant the ring gear assembly from another diff.
I sandblasted and painted my diff, and the roller bearings got some sand on them.
So the ring gear assembly has 2 bearings already. They're insanely expensive, so I just purchased another diff from marketplace to use the ring gear assembly from it.

My E53 is 3.0 2002. The diff I purchased on ebay seemed to be E53 2003
As I started taking it apart, I realized the marketplace differential had a different spacer/snap ring.

The original rings were 3.68 and 3.82. I expected the marketplace diff to be the same, it looked the same from outside. However I noticed it's snaprings were 3.82 and 3.74

The ring gear assemblies also have different part numbers, so I'm kinda confused by all this.
I decided to take a chance and transplant the ring gear assembly along with the snap rings to my painted case, but I wonder if there are going to be issues.