I'm not sure exactly how yours works, but I've never seen one that got feedback from the trailer brakes.  If it is starting to apply them and turning off the controller stops the problem.  it would seem logical the problem is on the controller end.

The best way I have found to diagnose problems is start asking questions and then look for the answers.   Is it possible the problem is not the controller but where it is getting signal (power) from?  If the controller is getting a small signal on its input, would it cause a gradual application of the brakes?