I use 12v all the time while traveling, but its always "pre-cooled" before we depart.
And mine only runs on 12v when the truck is running, it will not run off the battery with the truck off, even if I force it, it beeps in error.
So when its set to auto, when I turn off the truck the fridge switches to LP. Plug into shore power, and it runs on 120v.
The most manual interference I have done, is forcing it to run on 12v only when we depart, so it doesn't kick to LP. This is typically only gas and food stops, with little to nothing in the freezer. Everything is plenty cold at our destination.
Finally, you can run a 14AWG wire pulling 15amps @ 12v over a 10' run per spec. So whatever the problem is, a larger wire will not help unless the current wire is getting hot to the touch. Warm is not abnormal.