Personally I think you may be 'flogging a dead horse' I think you may run across the common problems with trying to control 1ph motors by VFD.
I would think alot depends on what point the motor is designed to transition over to squirrel cage induction.
The fact that you could be moving in and out of repulsion/induction at different points of the rpm scale may prove to be an issue, you have the VFD already so It would not cost much at this point to try it while monitoring the result closely.
Unless you want to keep in its antique state, I would have thought the best bet would have been to put a 3ph motor on, or one of these higher quality DC treadmill motors available you can get really good KB DC 4 quadrant controllers on ebay for ¢ on the $.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.