My initial idea was to spin up the ball and then restrict the gyro to one rotational axis to see if it would generate enough force to precess the operator (me). Unfortunately, the ball requires constant energy input or it quickly slows down, and the time needed to cage one axis (using a couple of threaded bolts) is enough for it to lose a good deal of its momentum. So that idea is out.
However, the forces and motions involved are sufficiently interesting that it's probably worth taking it onto the flight and seeing what happens when you spin it up in freefall. So it's going on the list of experiments I'm trying to get approved.