Thanks for the pointer to those VFDs. They are expensive, though. For many tools, the VFD could cost more than the tool.
Yeah, the solutions offered to the OP of this thread are a lot more practical than a single-phase VFD. But they might be useful to those interested in building their own powered lathe. With one of these, the mechanical alignment issues with multiple pulley diameters and wooden pillow blocks aren't an issue.