Welcome to the Heartlland forum......a lifesaver and tons of "sage" wisdom.
Our BC is in storage too......I drive by on my way to work the day we are heading out and turn on the fidge, propane and battery, (making sure nothing else is on), that way she is nice and cool when I hook up a few hours later. Yes, we travel with it running on propane. Just be aware of any tunnel restrictions wherever you are traveling.