Running a 3 way ref. on DC is a "last resort". I think the 12v element in those things pulls something like 30 amps or so. That's about 360 watts so around double what your solar panels will be producing.
The propane burner is probably around 1,500 BTh per hour which translates to about
440 watts, that is, nearly 50% more than what the DC element will do.
I have no idea how accurate these numbers are for YOUR particular fridge but there should be a plate on it somewhere giving all the details so you can do your own calculations.
