I found a review posted by 'grimagog'? for a Mark Kelly controller applied to a Papst 3-phase motor. His claim was that having the ability to "tune" the current via the conroller leads to a quieter motor and (back on topic) improved speed stability.
Mark Kelly posts over at the DIYaudio forum occasionally and appears to be extremely motor-knowledgable. Jim Hagerman was toying with the idea of a new 3-phase motor controller as well.
I've got to believe that a multi-phase AC motor should be easier to design for speed stability compared to a 2-phase or single phase motor. More continuity of pulse per revolution, for sure. Certainly much of heavy industrial motors are 3-phase, so I think the math is pretty well-understood. But since most of us live where the power coming in over the wires is not 3-phase, some kind of controller is needed.
The Papst motors discussed above use a 4uF cap to provide the appropriate phase delay, to "trick" the motor into sync. I wonder if atmasphere has any tricks for improving the motor performance on his tables?
I've had good success with some of those grand old tables by micro-polishing the bearing balls, and improving the sleeve's ability to retain oil via fine cross-hatching at 1500 grit. The Rabco tables were interesting in that they had a spiral groove to "pump" oil back up the sleeve to keep a nice continuous lubrication film. With the right lube viscosity, these things would spin for several minutes down from 78rpm. I think the Empires were the same way.
So a nice even motor and nearly frictionless bearing = speed stability? (carefully avoiding the drive question here)