I don't understand why you are doing what you are doing. In the larger scheme of things, the electricity (12 volt) to run the board/valve is negligible. If you are going solar, why not consider running the fridge on 120 volts through a 120 volt inverter, solar panels, controller, and a battery bank, (probably 4-6 volt wet cells) eliminating the need to use propane at all? (at least for the fridge) IMO, you could do that with 3-140 watt panels (if you have room) and have plenty of solar power for most everything else too. You don't state what vehicle you have. (maybe the clue lies there)
Chum lee