Rather than allowing the gray to back drain into the black tank, buy a cap that has a garden hose connection in it, and get yourself one of those small blue tanks with wheels to catch your gray water. Leave the black tank valve closed, and the gray will flow into the blue tank.
Doing it the way you describe will force you to have to find dump stations more often, and at some point you're going to have to take that cap off to connect the slinky hose.
As far as making it up the mountain roads, I see no reason why you wouldn't be able to make it up or down any of the paved roads there.
:):)
