Lathe control, can it be done?

From what I am seeing, as the potentiometer changes its resistance, the reference voltage changes as well. This reference voltage is what is read by the rest of the circuitry. The resistance is not the parameter used to adjust motor speed, but is used to adjust the output voltage of the stage. This voltage reference is then fed as an input to the next stage (however it works to adjust the motor speed)

I think, and a strong I THINK, what you are trying to do is actually adjust a voltage that is fed to the rest of the circuit. The potentiometer is able to accomplish this by adjusting an internal resistance, which then adjusts the output voltage.

I believe your goal should be to adjust the voltage differential between these two points circled in red for the max speed adjustment

As a separate question when looking at the "Reference voltage circuit" diagram picture shown. The 50K pot labeled P3B, the arrow INTO the pot, comes from where? (Is it from ETI/C3J on the first picture?)