Since you didn't make any mention about an idler motor, I am going to assume you have a static converter (If I am wrong about that, then ignore the rest of this--sort of).
An off-the-shelf static converter is about the worst thing you can do to a motor because all it is, is a motor starter. Once the converter gets the motor spinning, it cuts out completely and leaves the motor to single-phase.
A balanced-static converter also uses run capacitors tuned to the characteristics of the tool motor, and will provide an output fairly close to that of a rotary converter.
As long as you are going to have to replace the start caps in your converter, you may as well spend a few minutes and turn your unbalanced converter into a balanced converter. To do this, you leave the start circuit as-is (after replacing the damaged caps), but simply add a couple of caps between the two source phases and the generated phase.
I have an article describing how to do this at
http://www.waterfront-woods.com/Articles/phaseconverter.htm.
