We rarely use the 12Vdc on the fridge, even when driving. It doesn't take long to discharge a new battery when stopped. We pre-cool the fridge on 120Vac and only put in food that's already cold. We can easily travel 8 hours in summer temperatures (80-95 degrees) without any problems. The propane flame almost always blows out when traveling so I don't bother with that.
Remember that the electrical current has to have a good return path to the source (e.g. battery/alternator). Increasing size of the vehicle and trailer's charge line to 8AWG may help some, but unless you also increase the size of the return lines (misnamed "ground"), you won't get much benefit. Think of the wires like water hoses. You can upsize the supply to a fire hose but if the return is through a garden hose you're stuck with the garden hose capacity.
2004 Toyota Tundra SR5 (V8, 4WD, TP, TRD)
2005 Fleetwod Allegance with axle flip
Honeywell 2000i Generator
Me, DW, DS, DD, & Chicken-Dog