People here can get pretty snarky (for lack of a better term)... don't let it get to you.
The only thing I could think of aside from a mechanical piggy-back system to move the pots would be something like a mosfet/opamp voltage controller or source that when fully on, produces the high end of the voltage range, and with a PWM signal generated by the arduino, the voltage can then be varied to its minimum range. This would be a new approach to the old tech. But would require atleast a few cups of coffee for damn sure. You said half is 250vDC. Since we know its 5hp, we can find out what the stall current is. You'd need to ask your electronics buddy if there are any "impedance matching requirements " i highly doubt it, but with old mechanical systems, upgrading to new-age controllers, you never know... If you're interested in seeing if this avenue is possible, I'm around!
BTW I appreciate the time you've spent doing your homework. I have many hours working mills and lathes so these projects are always cool to me to go back to my roots!
Edit: never mind about the stall current. Its not driving the motor