"cost-effective solution"
Probably only if you already have the bits.
"It's not actually boosting the voltage so much as presumably generating the additional phases."
Agreed. From what I recall my thinking went roughly thus:
Feed power to one winding and you have effectively a single phase 2 pole induction motor. Put crudely these work because the rotor becomes a 2 pole magnet which is dragged around by the stator field which keeps changing direction. Motors are also generators so we have a 2 pole magnet rotating inside a 3 phase stator. This is an alternator and since everything is vaguely symmetrical the winding voltages ought to be similar.
At this point the project went into 'suck it and see' mode and having achieved success further research and analysis went into the pending tray.
Obtaining waveforms might be difficult. I'm not sure I still have a high voltage probe and I certainly don't have a current probe. The last time I tried to get a current waveform in a power line using a small series resistor I forgot to remove the earth from the scope. Result – one destroyed probe and half the shop floor went dark. It's always the little things that get you.
It turns out I lied in an earlier post. I have found the basic schematic I generated for construction purposes and have uploaded a copy to my album. Treat with caution – e.g. no protective devices are shown.