Hey, Had the same problem with my 97 320i. It has the jatco box as well with a drive shaft that doesn't have the rubber gibbo at the front. Was real problematic under moderate/hard acceleration, used to get a hell of a shake around the 30-40kph until one day it decided it was going to do it all the time until i got to about 50kph.
Just got into it this weekend. turns out my drive shaft hanger bearing had fallen to pieces. the rubber that surrounds the center bearing had split causing the center of the drive shaft to move up and down under acceleration.
Also a good idea to check all 3 universals while you have it off (mine were ok). had to remove the exhaust, then the heat shield and finally i could get to the drive shaft.
Hope this helps with your problem.
