Also search for E23, E28, late model E24 (>'83), Z3 and 318Ti diffs. They're all compatible, if you have the correct rear cover and output shaft 'cups.' Rear diff covers are not the same between 210mm large case, 188mm medium case and 168mm small case. I have a medium case E30 rear cover with a good bushing if you can't find one cheap enough.
I'm running a 3.73 clutch LSD in my '91 318i (originally from an '87 325iS) and a 3.46 torsen LSD (from a '99 Z3 2.3) in my 635CSi.
You can also get a diff rebuilt with any gearing you'd like if you have a friendly & skilled mechanic locally. I usually look for a shop with cheap eurotrash exotics like 90s Landies, Alfas or a FIAT Brava in the front lot. Replacing the front bearing & crush sleeve is a pretty simple affair but setting up the ring gear lash, side shims, ramps and clutch packs requires expertise and special tools.