Are you sure about the radio running off the chassis battery? Mine, and others I have seen run off the house batteries.
Another thing that will run the house batteries down as well as propane is the Girard demand water heater. Even with the store/use switch in store, the Wh will run from time to time, if it gets too cold. It is a feature to keep it from freezing.
The only way to stop it is to shut it off in the outside panel.
Running batteries dead isn't great but it won't ruin them immediately. Mine have been run clear down twice and they are still fine after three years.