I'm an electronics tech of sorts in real life so I'll try to offer some assistance. First of all, why not just change the motor? I doubt that it is more than a fractional HP unit. The internal electronics, even on quite sophisticated machinery, are usually run from a single phase of the incoming lines so that portion of the machine shouldn't be an issue.
If the motor is an integral part of the unit, another method of side stepping the problem is to use an electronic inverter drive. Smaller units (<1hp) are available for a couple of hundred bucks these days. Then you just run single phase into the inverter and get 3 phase out. The inverter controls can be wired to the start/stop relay presently in the balancer to start and stop the drive as needed.
I'm not a proponent of rotary phase converters, they are noisy, inefficient and produce poor quality power. I would go to great lengths to avoid thier use...