It will work fine.
The only thing I would think about doing is putting a subpanel between the shore power inlet and the main breaker panel, and an automatic transfer switch between the subpanel and the main breaker panel. Set the transfer switch to default to shore power. On the subpanel move the circuits for the AC, converter, and electric water heater element.
As soon as you unplug, the inverter carries the loads, you just have to remember to switch the fridge to gas. Everything works BUT the AC, converter, and electric water heater off the inverter. If you want one of them start a generator, or plug in to ac power.
