I would put a heavy gauge wire to your batteries. Of course how every your ground is run needs to be just as heavy.
It doesn't have to involve your converter charger. Put a solenoid in on the hot wire so it is only connected when the ignition is on. I am sure there is this or that about charging completely dead batteries from your alternator but I personally would not be concerned. Actually you shouldn't discharge your house batteries lower than 12 volts or you will severely shorten their life in the first place.
How you would go about this is all about the umbilical on the camper now and how heavy those wires are. If they are nice and heavy gauge then you just need heavy gauge to your plug in. If not you will need to bypass the umbilical.
Now a good way to keep your batteries charged is solar and that is way cool but takes some work. But I love my solar I installed on my TC JMHO
