I had the exact same problem on my 1987 320i.  Driveshaft centre bearing
eventually packed up and the driveshaft rebuild cost me the equivalent of
450 US$.  This included the rubber driveshaft coupling.  Unfortunately the
ID10T that rebuilt it used spares form I don't know where and the car had a
vibration at 120km/h.  Sent the car back, but ended up having to live with
it.  They insited the vibration was caused by my tires being out of round,
which I had balanced with no effect.

6 Months later I took my car to a clutch/brake and driveshaft specialist who
replaced the pirate parts on the driveshaft with genuine BMW parts, and
another new rubber coupling.  Now the car is running smoothly on the same
set of tires.

The jerky rocking when you lifted off the gas, was much better immediately.
You may also look into replacing the CV joints on your two sideshafts, as
this may also be a cause of some play.  I very much doubt that you have any
problem with your diff.

MW