How did the swap go? I've done this many times, only for SVX, using a non-lsd 3.70, 4.111 and 4.444. Swap in the SVX lsd [fyi-different than XT lsd] I have had good success using all the donor diff parts, including end caps and shims. To double check, two things I've learned. First, before disassembly of diff, rock the input hub, and note the travel, sound and feel. If the clearances are good in the converted unit, the feel will be the same. I've used gear marking compound to confirm, but if it feels right, and you use the complete 3.90 with the 3.70 lsd only, you should be okay.
That said, I need a 86 or newer 3.70 donor rear diff, doesn't have to be lsd, maybe one of the 'left-overs' from a 3.90 conversion. Can anyone help, I'm in Southern California.