There is no need to keep the battery on constant charge. Having killed a dozen batteries over the years (mainly on boats) when charger malfunctions boiled them dry. I just full charge and switch the battery(ies) off. Turn 'em back on when needed. Mine will go thru the winter and come out at 70% charged; no need to bring them inside and risk acid spills. But it gets quite cold here and self discharge slows as it gets colder.
My understanding of LP cylinder valves is the same as Old Bisquit's: There is a backseal that is engaged when the valve is fully open. I open my valves the first time out during the season and shut them off just before removing the tanks in preparation for winter indoor storage.
-- Chuck