And to update this, it works.

I was bored tonight, and with the CNC lathe still out of action so no need to worry about the unfiltered output blowing up that, I bodged in some wiring to test it using the 4.0KW 240-380V VFD I already have.
The milling machine starts far better than it would through the rotary converter, with only a very slight dim of the workshop lights.

I did want to measure the output voltage, but my multimeter really didn't like the unfiltered output as it scrambled the display, so next purchase is a suitable sine wave filter. If that works, a bigger VFD and sine wave filter will be purchased, and a more safety conscious and user friendly control system that doesn't involve a step ladder next to the open terminals to hit the start button on the VFD

If I'm bored again tomorrow, I might drag out the oscilloscope, just to see what kind of output the VFD is actually achieving.