Having previously had a 3 way fridge in a Trailmanor, here is my input:
It is a 3 way fridge for a reason.....it is meant to be used on 12 volts on the road. You don't have to worry about the downsides of leaving your propane cylinders on while in transit.
There are some inherit problems that can occur, though. If your tow vehicle does not have a 12 volt isolation circuit (the isolation circuit cuts the power to the trailer when the TV switch is off) to the Bargman plug, it could run down your TV battery during extended stops. It would take some time, as both your TV battery and trailer battery would be involved.
If your TV has an isolation circuit, then you could more easily run down your trailer battery.......just a single battery instead of 2 batteries. Again, that would probably take several hours, and not usually a problem.
I installed a 30 amp blade fuse on my battery hot wire. If I were going to stop for lunch or some other long stay, I would pull the battery fuse and lay it in my truck seat. I would install the fuse when ready to travel again. Yes, the fridge would be off during that time, but those little puppies hold the cold in pretty good, so an hour or so won't make a big difference.
Chap , DW Joy, and Fur Baby Sango
2006 Ford F150 Super Cab 4x4
2008 Surveyor 263