I haven't seen one in a plant in about 40 years. I would be surprised if you can find parts for the original model.
A Google search shows that Dynamatics are still made, and I am very surprised!
Many larger motor shops still repair eddy current clutches but, by the time you add in the poor efficiency, the cost of repair is is prohibitive. The energy losses are roughly proportional to the speed turndown times the motor kw. So, for example, assuming a typical constant torque load, a 30hp motor clutch running at half speed delivers 15hp to the load and wastes the remaining 15hp or about 10kw as heat. At today's electricity prices, that's pretty ugly unless it's winter time and your building needs the extra heat!
A VFD and premium efficient motor will often pay back the initial investment in 15-20 months in energy savings alone.
These numbers are not as ugly if the load is an increasing torque type like a fan or centrifugal pump but, even then, the VFD is generally the choice.
The biggest problem as far as the "running away" condition on Dynamatic drives was usually caused by the center bearing trying to fail. It could also come from the SCR in the controller module overheating and near its end-of life. Some of the earlier units used a tube so SCR failure would not apply to them. However, the tube could short internally intermittently. As others have said, you should replace the Dynamatic units with a good VFD at failure time.
We used to pull all the Dynamatic drive motors annually at summer PM shutdown to just replace the center bearing and dip the windings to seal out moisture. They were used in wire drawing machines and the drives stayed damp from wire lubricant spray.
Edit:
Normally when the center bearing fails, the output shaft just locks to the rotor and runs at full speed the moment the power mains to the motor are energized.
If a cooling down period restores normal function for a few hours, the controller is probably the issue.