I have a question. Has anyone actually used a VFD to power a higher-voltage motor through a transformer? I'm wondering if the transformer, which was designed for a specific frequency (50 or 60 Hz), can pass the speed-control variables on to the motor reliably. The VFD works by changing the frequency to the motor. I have mine set for 10 Hz to 90 Hz, but it can go up to 200 Hz.
I'm pretty sure you would have no problem raising the voltage from 220 to 440 single-phase through the transformer and then using a 440V VFD to change single-phase to 3-phase and control the motor speed. Just don't know about using the cheaper VFD ahead of a 3-phase transformer.
The costs could balance out - single-phase, lower-voltage VFD with 3-phase transformer vs single-phase transformer with higher-voltage VFD. All things being equal, I'd up the voltage first, then convert to 3-phase with control.