Those batteries will be good boat anchors unless you can get them properly recharged for many hours using that charger. You can check with an hydrometer as things progress for getting them up to 1.275 or so.
You have the battery wires to the dist panel now, so all you need is a converter on the battery posts. That will allow the converter to run the dist panel up the battery wires.
The DC distribution location would be hard to relocate, but the converter (deck mount type) can go anywhere you can get 120v to it and get the output to the battery bank. Usually you want it close to the batteries for less voltage drop, but on shore power that is not so important.
You can cover the existing power centre with any vented panel from a hardware store. Just move the converter to someplace else.
Our Class C has the 6300 under a dinette seat. The battery compartment is under there from outside. I yanked the 6300 lower portion, jumpered the 6300's split fuse panel so I could keep it as is, and put a deck mount converter under the seat plugged into a 120v receptacle I added in there, and wired the converter output to the battery bank. You don't have to put the converter in where the "lower portion" was.
