You are correct in using the #10 wiring. The internal wiring is specified by the manufacturer and installed as they determine to be correct, based on the amperage rating, and all the name tag nomenclature. 30 amp breaker is appropriate.
Is the motor, by chance, a dual voltage motor. Can you set it up to run on 240 volts? Less amperage, smaller wire needed, and smaller ocp, although it would be a double breaker.
Is the motor, by chance, a dual voltage motor. Can you set it up to run on 240 volts? Less amperage, smaller wire needed, and smaller ocp, although it would be a double breaker.