That's an odd one. If it's always at the same RPM regardless of gear it's unlikely to be the drive shaft or differential. That does sound like a center support bearing, guibo or diff though. Can you pinpoint if it's coming from the front or rear?
It's tough to inspect the driveshaft as two heat shields, sub-frames, tie braces, fuel tank, etc. are in the way. But at a minimum I'd put the car up on stands and make sure the diff doesn't have oil leaking from the input shaft. The output shafts seem to leak a bit on every e30 I've seen though, that's never caused a problem for me.
When I bought my 318i it had a similar problem...the small case diff's input seal was destroyed and driving the car sounded like a gorilla was pounding a Samsonite under the rear seat.

I fixed my problem with a medium case 3.73 LSD from a 325is at 266k miles. According to the PO's records, it had been replaced at 192k miles to the tune of $788. Mine cost $280 AND had an entire car attached to it for spares... :cool: