I would say you definitely need to pull the brake drums and inspect the brakes.
The Prodigy P3 brake controller will only apply as much brake as needed. Not likely the controller is applying too much brake.
I suspect the brake shoes are not returning when the controller is going to zero output.
Look for a missing or very weak return spring / springs on the brake shoes.
Grease on the brake shoes is another possibility.
Also if you are touching the brake pedal enough that the brake lights come on then the brake controller will apply some braking depending on your boost setting.
I have seen vehicles going down long grades when the brake lights never go off. I suspect they have their foot on the brake with no pressure but enough to turn on the brake lights or possibly they are riding the brakes.