I am not going to get into the propane danger debate but I have to state for the record that propane under the right conditions is extremely dangerous. Since it boils at ~-45F it requires pressure to keep it a liquid and once released it expands to like 270 times it's volume as a gas. I had a working acquaintance keep a cylinder in his garage until one day he went in with a lit cigarette and found out the hard way that it had been leaking. Blew up his garage and his house and almost killed him. Really he should have been dead but survived and required multiple skin grafts to look halfway normal again. Just remember propane can also leak from the PSV and not just the valve or regulator. Dangerous stuff.. Enough said.
The biggest problem running your fridge on DC is not the heater because with a simple change of the element and rectifying the AC signal that goes to the heater now and it would essentially be running on DC. No the problem is the temperature feedback circuit that tells it when to turn off and on. Instead of reinventing the wheel, I would find a tri powered circuit board from dometic that was and bring a fused DC circuit to that board (and change the heater out with a DC element). This way you could run it going down the road on DC instead of propane when you wanted.
The biggest problem running your fridge on DC is not the heater because with a simple change of the element and rectifying the AC signal that goes to the heater now and it would essentially be running on DC. No the problem is the temperature feedback circuit that tells it when to turn off and on. Instead of reinventing the wheel, I would find a tri powered circuit board from dometic that was and bring a fused DC circuit to that board (and change the heater out with a DC element). This way you could run it going down the road on DC instead of propane when you wanted.