It's a permanent split capacitor motor so it already has one to generate the phase difference. Yes, changing the capacitance would alter the speed a little, but not that much, and certainly nothing like as much as a 3 phase one running from a variable inverter. Not to mention that it's not adjustable on the fly.

Plus you run into the problem with single phase motors that most methods I'm aware of for changing the speed tend to make the torque fall off a cliff very fast, which means they stall and/or overheat horribly.

All in all the 3 phase approach is preferable, irritatingly enough. But I do at least have the most expensive part sitting in the garage! Just need to get the pump.

pca