Hi Anthony,
You might try to measure the resistance of the two winding. If both
windings are the same guage and the same resistance, it might not
matter which one you use for the start winding. Leaving them on all
the time may harm the start capacitor. I dont think they would fight
each other since one has a different phase from the other (due to the
capacitor) and syncing is not an issue unless you modify the motor
for sync operation. If you experiment with the windings, you may
want to fire up the motor for a very short time, power down, and see
if the windings are getting warm. Repeat this for progressively
longer times until you are satisfied the motor is running
properly. If you suspect it is not right, you may want to swap the
two windings and try again.
Gerry R.