I did find this cool video of a toothed clutch:
The clutch mechanism I'm designing is not so complicated that it would cost anywhere near the $600 would cost for two more high quality servos. Besides, for $350, I can get a servo motor rated at 126 lb-in with the controller (shared among other servos). That would allow the single motor system to be cheaper and still faster than a three motor system.
I plan to use a couple simple solenoids to engage and disengage the drive.
Besides that, it's basically a metal disk, and a pulley.
The pulley would be connected to a belt drive or whatever drive I end up using.
The metal disk would be permanently attached to the motor shaft.
When the solenoid is on, it would engage the pulley to the motor shaft. When off a simple spring (or maybe a second solenoid) would pull it back into a locked position.
Solenoids are dirt cheap. The rest is just a few simple metal parts.
The servo motor would be stopped whenever engaging or disengaging, and could be slowly started to make sure the clutch engages well before it starts moving.
The servo motor itself controls speed and direction. So, no need to worry about that. I think this solution is much better than spending 600 on additional motors.
Seems feasible to me.