We ran a poll here awhile back asking simply "do you travel with your
fridge on LP or not".
80% of the poll responders said yes.
You can read some discussion here--
Do you run with your LP on or off
This question comes up often and there are many other threads about it.
We used to have a trailer with a 3 way fridge as you apparently do.
I also found I arrived at my destination with less than a full trailer
battery if I had the fridge on DC operation.
We switched to running with LP on and problem solved.
Now days, very few fridges come with 3 way power and I believe it's cost
saving plus the huge battery drain that's the reason.