To clarify, what you need to achieve is to reverse the polarity of one winding relative to the other. It does not matter which one you reverse because their polarity relative to the mains supply is immaterial. All you need to do is identify the two leads belonging to one of the windings and interchange them.
If you can identify four leads from the windings, by disconnecting them and checking for continuity between them you can make them up into pairs. E.g. if you call them 1,2,3 & 4, and you have continuity from 1 to 2 (one winding) and from 3 to 4 (other winding), then reconnect leads 1 & 2 whence they came but interchange 3 with 4. I would expect Red/Black to be the run winding, and Yellow/Blue to be the start winding, with the starting switch internally connected in series with one of those leads. In this case, interchanging blue and yellow will reverse the motor, but you should do the continuity check and try to follow the leads in case my assumption is wrong.
The start winding and run winding retain their original functions, but the phasing of their currents is inverted so as to produce a magnetic field that revolves in the opposite direction. Once up to speed and the centrifugal switch opens, the motor carries on running in whichever direction it is already running.
E2A: Have you looked inside the covers you have removed? There is often a wiring diagram stuck on the inside.