The fact that the motor started and ran normally with acceptable power in one direction told me there was nothing wrong with the centrifugal starting switch, the start capacitor, or the run capacitor. The failure to operate in the other direction still seems to me to be caused by a failure to successfully switch whatever winding is being used to reverse the motor, probably the start winding as it won't try to start. Before you start field stripping the motor, determine what reversing switch you have. It should be wired something like this. Caution: this may not be your exact switch, you will have to determine what you have. Then measure the voltage between the switch connections in both directions. Measure between #2 and #3 and between #4 and #1 in one direction. Reverse the switch and take the same readings. I'll bet you a beer you won't have 220 volts for all four readings.

The following diagram illustrates what I mean.