1985 .... Torque is what brakes parts. X amount of torque goes in to produce acceleration but there is Y amount of dead weight and traction resisting that torque. If either are to great compared to the other something has to give. That'll either be a weak point in the drivetrain or traction. Traction almost always looses. It doesn't matter how many cylinders are producing that torque, it's just a number.
The question of the ability of the BMW rear to withstand the power of a V8 has long since been put to bed. In race trim Bemmer engines produce a lot more power than the V8's used here, and the rears handle those without problems. These cars are also lighter than the original Beemers, so that reduces the dead weight, and in some cases traction that resist the torque. Yes with enough abuse anything can be broken, it's just a case of keeping everything within the limits. BDR's have been running with 600+ HP and the rears have stood up to it, the tires ..... well that's different
Bottom line is the rears don't break with the power and traction available, even with an FE.
Dino - sounds like it MAY be an easy fix.