Looking at your diagram in the first post this is how I think the motor is wired internally.
U1 to U2 is the main winding.
The auxiliary winding is between Z2W2 and the point where the two capacitors are connected together..(Yellow wire to the inside of the motor.
The centrifugal switch is connected between V1 and the side of the 150 uF capacitor with the black wire connected to it.
You can confirm if I am correct by doing the following resistance tests.
1 / measure the resistance between the black wire connected to the 150 uf capacitor and V1. This reading should be very close to zero ohms.
2 / Measure the resistance between U1 and U2. this should be quite a low resistance. (Less than 20 ohms,)
3 / Measure the resistance between Z2W2 and the red wire between the two capacitors.This reading should be quite low but a a bit higher in the reading from test 2
4 / measure the resistance between U1 and Z2W2 This should be a very high resistance probably more than 20 Meg ohms which is probably higher than you meter is capable of reading.
If these readings confirm my theory then connect the output from the reversing switch whose polarity is the same in forward and reverse to U1 and U2
Connect the output from the reversing switch whose polarity is reversed between the forward and and reverse positions of the switch to V1 and Z2W2.
Les.