You're missing a possible cause - broken engine or rear tranny mounts. Check those first. Cheap, easy.
After that, check for severely worn parts in the shift linkage. Unless it's been rebuilt at some time, you can bet they are very loose. There are several good threads on R&Ring the linkage. You need to drop the exhaust and driveline to do it right.
Swapping in redline MT-90 is a good thing to do at the same time.
Bellevue WA
90 535iM - not much stock remains. 3.7 liters, ported head, cammed, 3.73 diffy, M5 brakes, MAFed, yadda yadda yadda
86 Porsche 951 - Track Toy