It's a bit of a drive for you, but if you wanted to come down I'd be happy to diagnose it for you to make sure. I have all the electrical goodies to check batteries, chargers, etc.
Easy way to tell if you don't have a meter - when you plug in the camper to shore power, do the lights get brighter? If not, something's definitely up with the converter.
As far as charger - this is a bit expensive, but it's a top of the line fully programmable 3-stage charger, and 2KW pure sinewave inverter and built in transfer switch - kills 2 birds with one stone. I have one, it's awesome.
Xantrex Prosine 2.0