Bill,
Just fixed the same problem in the Beaver, all at once it was filling the fresh tank very slowly. Though it was the Asco solenoid fill valve, figured something in the seat. Opened it up and was fine. only other place water can back flow in the fresh tank would be the pump. Disconnected the inlets to the Asco and water pump and turned the city water on and the water was slowly leaking back throught the pump. Went down to local Ace and got a 1/2" inline check valve and installed it on the discharge side of the water pump, problem solved. I think one of the valves is leaking in the water pump, it is a Remco AquaJet11