Check these two sites out
First link is wrong where you see the S15 6MT ratio, it is 3.692 NOT 3.392.
You wants that will fit an R200 unless you are implanting the entire diff into the subframe (involves cutting and welding)
The low-down on S13 Diff options? Archive and FAQs
www.zilvia.net
.
Please do more research before you do anything else. You should know what's involved before you go down a path.
I'm sure the BMW trans was probably plentiful and cheap, but you should have talked to the other guys who did it and ran into the same exact problem as you.
Personally I would have done the Z32 trans. Same ratios as S13/S14 but stronger. I would have bought a crappy one to rebuild and installed that before the BMW trans but that's just me.
Let me know what you end up doing