The trick is to get a really good spinning mass on the airplane within the rules.
Fortunately, there is a really good angular momentum source within reach of just about everyone reading this entry -- the hard disc in your computer.
So the plan is simple: stick an old (preferably high-rpm) disc drive into a cheap USB enclosure, and replace the wall-wart with a 12v battery.
Planned demonstrations: conservation of angular momentum (turn on drive, it spins one way, operator spins the other) and gyroscopic precession (spin up before we hit zero-g, then tilt the drive enclosure)
As always, your suggestions for improvements and additional demonstrations are appreciated.