Looks like you might be able to buy a new pot for under $50:
https://www.radwell.com/en-US/Buy/ALLEN%20BRADLEY/ALLEN%20BRADLEY/33173/
Yeah I had seen that in the past, but with no way to order it. So I just gave them a call and they said if they had any the web page would list how many that had and a way to order it. They don't have any and checked with their counterparts who also don't have any. They are a discontinued item and have been for years unfortunately and from my understanding were specially made for the lathe manufacturer. 
No worries, how the spindle speeds are obtained, especially back when this was designed is intriguing. For those of you who understand electronics much better than I, I can only imagine how interesting this might be.
One Monarch 10EE owner describes the pot as:
"58C1 Clarostat with half of the windings shorted."
By "windings" I think they mean it's a wire-wound pot.
Since the pot is dead, I would disassemble it and see if the resistive elements can be repaired or replaced.
There are also two still available from this set of 5:
https://www.ebay.com/itm/324730119011
Thank you. Custom made DC motors. Interesting.
Paul
I bought the first one from that set. 
How did you figure the motors were custom made? I didn't know that.
Look at the name plate. WOUND spec opd. I don't know what opd is but I know what spec means. So, if you find out what an OPD is that would be interesting. I once had a motor that said 120 V DC FWB that confused me for a long time. The FWB means Full Wave Bridge rectifier. So, it could run on pulsating DC and create the rated torque without vibrating from the pulses.
Paul
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That's a lot of power in the pot. A quick calculation puts the 50k pot at just below 1.25 watts. Which is kinda OK since the Type J pot is a 2w device.
But I can't think of a solid state replacement for this pot. I guess one could control it with a motor or maybe a RC Servo.
Well, if I had asked Google, first, I would have known what OPD means!
An open drip proof or ODP motor is a type of motor that typically runs cooler and does not overheat. Due to the fact that the chamber has open vents and air can flow directly over the windings, this open drip proof motor tends to be slightly more efficient because the windings are cooler.
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