I bought a Speedaire 2 HP compressor from a closing factory, from a very nice owner, for $50. The compressor was a backup compressor and, evidently, did not run much.
I also bought a 2 HP single phase motor from Dave at Pioneer Industrial Services, for $10.
You can see and compare the 3 phase pictures with single phase pictures.
It is important to note that the single phase motor is thermally protected. The thermal overload relay that was on the compressor originally, tripped all the time because single phase current is higher than 3 phase by sqrt( 3 ). So I simply disabled it, reasoning that overload on the motor itself should be perfectly good. Everything is wired straight to the contactor, bypassing external overload.
It cuts out at about 125 PSI and starts pumping a 100 PSI. That's how I set it.