I had speed control issues on my BC2000 that I worked on years ago. Looking at my emails I ended up replacing the motor and that fixed it. There are some electrolytics on the motor control PCB (inside the motor case, where the potentiometer is) that you might want to check first. Not related to this case but still I'll copy-paste this here for posterity: "There's a resistor near the voltage regulators at the cooling fin. It can burn in severe cases of overload and it will cause the motor to run at slow speed under load (wind/rewind) and eventually grind to a stop. It's R8 and either 4,7 or 5,1 ohms". (Source: emails with Martin ⭐  in 2008)

Is the belt running correctly on the barrel-shaped area of the motor pulley body? - Not on one of the pulleys flanges? Martin

Considered getting new motor, just don’t want to have the same issue if I do! I’ll check on that resistor too, thanks!   Martin, the capstan belt is correctly seated around the larger section, and the smaller belt is down at the bottom section, not wrapped around but pulled to one side.

If you are sure that everything else is fine, ask Danish Sound Parts for a good replacement motor. It may not be immediately available online, but don't let that stop you from asking. Martin