I have never thought of wiring a 3 phase motor as single phase. Don't you have to have a centripetal switch as well as the capacitor? I didn't like to reply in case Jazz came along and told me that was only for cap start and I was being silly

Why would you want a single phase motor if you buy an inverter? Surely it would drive the motor you have, assuming you put it back the coils back the way they were.