I went through my transformer book and I could not find a single phase Scott type connection, it just ends up as a single phase buck and boost.
You could do it with the proper capacitor inductor connection but the size on the capactiors would need to vary based on load. This would be similiar to a static three phase convertor that someone else had mentioned.
I think your better off to replace the motor or maybe go with a high end treadmill motor. I run a treadmill motor on my 12 x 36 lathe and have no problems.
Art B
PS That motor may have some value to a college as a lab motor.