I've looked at that diagram, but the two windings have the same resistance ... I thought start and run windings usually had differing values, also there's no sign of a capacitor ever being fitted to either motor, but I agree, the little I know of single phase motors says there should be a cap some where in the circuit.
The second motor has a seized bearing, so trying that is a non-starter. I think the one I'm tying is in OK condition given the windings are open circuit to ground.
I think I'll have to try linking Z2 and A2 and stick mains on either Z1 and A 1 or Z2 and A2 and see what happens.
This is for the belt grinder mentioned some time back ... I decided the treadmill motor was too small for use with metal, but the speed control would nave bee a major benefit, To that end I have a three phase motor which I'm toying buying an inverter for ... may be a better solution all round (with the exception of setting up the inverter ... they look very complicated!)