[reuelt]

I would just use a jumper cable suitable for 15amps to bypass the speed controller.
If the router can run at full speed when the speed controller is bypassed with a jumper cable, then BUY a new speed controller.
(I replaced my Hitachi M12V speed controller after testing that my M12V ran at full speed with a jumper cable)

 

[reuelt]

Still not 100% sure about wiring up the new one, for fear of frying it if I get it wrong.

Don't take off the existing speed controller yet. The new OEM speed controller will be identical so just follow the exact wiring. If you cannot reach one end of a wire like my M12V, I just used an insulated wire connector.to join an cut existing wire to the same wire in the new controller.