I guess they aren't all the same, my Dometic runs better on 110 than propane (faster cool down). The Norcold in the class A I had seemed to run better on propane. But it should run either way.
If it is only happening when you are moving, I strongly suspect there are some airflow problems with the outside (condenser) part of the fridge. Something is stagnating the flow up through the condenser when you are moving. I would try shielding the front 3rd of the exhaust vent as a start - you will need to experiment. One thing that would help is to know the temperature in the condenser space when moving and not moving. A suggestion would be to get an inexpensive remote temp sensor (the kind with an outside temp sensor on a wire) and put it up near the coils til you find the hot spots. See if there is any difference between stopped and moving, if so then experiment with venting to make it better.