This is an unusual situation as it is not a trailer disconnect issue. I don' think this is wiring issue. I think it is controller problem. The reason I say that is you know you have continuity on the brake line as you have too much rather than not enough brakes so you have plenty of current. The wiring has to be connected and intact or you could not have such severe brake activation.
It sounds to me like the controller has lost it's ability to properly interpret pedal pressure and deacceleration. I would take this to a Ford dealership to check the controller. A tech or RV dealer can verify you have too much current with minimal pedal activation, which you already know, but will not be able to test the controller further.
My two cents worth,
RVDA/RVIA Master Certified RV Technician
You think you're confused?
2002 F350 Dually, Rhino Liner, Edge Evolution (running in stock mode), 4" exhaust, 6.0 cooler
2010 F150 super cab, box stock, bed slide, ARE bed cover