Hi Drew,
Since no one else has responded i will add my comments.
Normally the later MZs rely on the rubber bushes to control movement and the steel bushes should be trapped firmly against the frame. In my experience (mainly with TS250’s admittedly, the steel bushes are relatively slack on the spindle. I would first make sure that the spindle nuts are done up really tight and the lock nut is also tight to ensure the spindle itself cannot move.
It would be worth removing the wheel and the shock absorbers. You need to make sure that you rubber bushes are flexing rather than the spindle moving.
Regards
PeterF