After owning 2 absorbtion fridges, one a 3 way which is older technology and a 2 way(newer) we always travelled with the propane on except for the times it was not permitted. I don't think we had a problem.
Now, we leave our fridge/freezer on 24/7 on ferries/tunnels/fuelling, anytime.With our lifestyle it is not uncommon to be camping on very uneven ground. We even stop on 12% slopes for extended times and the meat stays frozen and the beer stays ice cold.
It is not for everyone and you must be setup electrically for it but I have yet to hear of a compressor fridge burning up an RV.
There are alternatives.

12% grade for 1.5 hours. Could stay like this indefinately.Galena Bay ferry. B.C. April/13
Dave