It may not be the answer you were hoping to receive, I can understand.
But, the previous expert is spot on with the situation, there is no way to achieve a speed control on the motor you have in hand.
Even if there was a controller for that type of motor, it is a capacitor start and most likely has a centrifugal switch inside the motor.
This switch cuts out the capacitor when the motor reaches approx, 75% of its rated speed and then the motor runs on the run windings.
So, even if you had a speed controller to work on the single phase motor, you would have to run it at 75% speed just to get it switch from start to run. .
The motor is not designed for controlling the speed electrically.
Best to get a 1/2 hp 20 rpm gear motor for the application and it would run at 20 rpm output all the time normally through the gearbox.
Used these on swimming pool covers and other special applications