My understanding of the 3 way fridge is different than I read here:
About the best that can be achieved is a delta 40 degrees F and 30 is more realistic.
The reason they need to be level is to return the condensed ammonia mix back down the swirly tube without creating a liquid trap. The toss and turn of moving unit is enough to clear the tube of liquid.
The performance should be the same with LP, 12V or 120V as the limitation is in the refrigerant.
In our unit the flame will not stay lit in high wind (like driving down the road). Safety dictates having LP off at tank when driving.
It is a good idea to have a small fan on the exterior fins to help cool them for max temp differential. Ours is on a 90degF thermostat. Check for that thermostat and a fuse "Wagoneer".
Sometimes I will spritz water on those fins when we stop in the hot desert afternoon.
Recently talked to an all electric Van life guy who uses his 2000w inverter and a 120V college dormitory size fridge ~$200. Says with solar and 200 Ahr he can go 3 days without engine charging help.