Ok, I've been doing a bit more research on the hoofernet. I now think it is for injection braking of the motors, which are permanent split capacitor types. This would agree with my previous finding that one winding makes the motor go one way, the other makes it reverse.
I've been looking some more at the control circuit for one of the motors (the other one just has a switch). It looks as though for normal running, the 2 windings are fed through diodes, one to either side of the capacitor, both with anode to a winding, cathodes commoned and fed by a triac (I didn't look further upstream than the triac's opto-isolator). I would have thought the motor couldn't work like this. Can anyone suggest what's going on?