6 deep cycle batteries whether 12V or 6V is gonna be around 600 amp hours or more.... something capable of putting out 6-12 amps at FLOAT voltages (13.2>13.5V) should be able to keep up with parasitic and self discharge losses during storage.
Why not just run your converter off of household current with adapters. No need to buy anything if you have a modern 3 stage or better converter. If you still have the 2006 original converter...your money and your batteries would be better served by buying a modern 3 stage converter to take care of them on the road AND in storage.
Also... if charging your house bank does NOT bring up the chassis bank as well...you can install a trik L start device with 3 wires that will top up your chassis batteries AFTER your house batteries are full.
Ultra TRIK-L-START Starting Battery Charger/Maintainer
Hope this is helpful.