I cannot believe that I am the only one on this forum who is NOT comfortable with the propane on while in motion. I turn it off at the tanks. Every time the trailer turns a wheel.
The chance of a propane accident is tiny, but why risk it if it is not absolutely necessary. I watched a TT burn in the median about 10 years ago (after rolling over) and while I know there have been improvements in valves and controls, I'm not risking it.
We usually travel one day and then sit and play tourist for one or two days before moving on. On travel days the critical cold stuff goes in an RTIC (think YETI)cooler with blue ice packs and stays there until initial cool down of the fridge is complete at the new location.
Your trailer; your choice! I don't see it as worth even a very small risk.