I am not sure how the burner on your hot water heater works, but if it is like the burner in my refrigerator it could be the burner is clogged with rust. If so, try cleaning the burner and see if that solves your problem.
Its been a while since I was to Alaska in our fiver, but the thing I learned on the road was:
If you see road sign saying "Bump" you better slow down. It is not like in the lower 48 where a bump sign means a slight change in the road. On the Alaska hiway they only put a bump sign out when its a really big bump...
I am just taking a guess, but I would say that your RV refrigerator would not be a candidate for running on a device that converts 12 volt DC to 120v AC. Your refrigerator uses resistive heating to turn liquid ammonia to a gas. The current draw would too high. It would exceed your batteries capability.