I wouldn't think that any 3-wire controller will work. Now that you have it down, have you actually opened up the boxes and inspected the circuit boards and wiring? When it's on the mast, moisture can get in and corrode contacts. My guess is that most of the electronics is in the control unit. The unit on the mast should just be a synchronous motor.
The problem is that, they made these things too complicated. I have a old (1990s) Radio Shack rotator that I use for the same reason. It's a bit rusty, crusty, and a little noisy, but it always works. The whole thing is just two synchronous motors. You turn one, on the control box, and the other, on the antenna mast, follows suite. Couldn't be simpler. And, I even have a drawing with troubleshooting info. I think I paid $15 for it at a ham fest. You could always wait for the next ham fest and see what is available.
The Channel Master that you see on EBay is similar to my Radio Shack rotator . You won't have all of the bells and whistles that the RCA unit has, but it will probably work fine.