One problem I have encountered is that gyroscopic precession causes
the buffer to slowly turn. Even though it's on 3 rubber feet the force
acting on the buffer is pretty strong so the whole thing spins slowly.

Gyroscopic precession requires that the gyro's rotational axis be
displaced. If the buffer is just sitting there spinning, it's not
precessing. If the shaft is tilted while spinning, and tries to twist
90 degrees to the applied force as it tilts, that's precession.
Most machinery that walks around is suffering some sort of
vibration. The machine may jump vertically, or might have some mode of
alternating its weight between its feet while moving the free foot in
some direction so that it moves around. Balancing should be tried
first, then some soft material used under the feet to maintain floor
contact while allowing a bit of vertical movement. Or bolt it firmly to
the floor.

Dan