Others have said these and I agree, just to summarize:
Wiring is often an issue. Is there anywhere you could relocate your batteries to that would shorten the cable run significantly?
True deep cycle batteries such as 6 volt golf cart batteries will give you more amp hours and will last longer. There are also true deep cycle 12 volt batteries but they're bigger and more expensive. (AGMs)
Charge voltage is definitely an issue. The 13.6 volts your converter puts out is a compromise between being enough to charge the batteries and not enough to cook them. Most 12v. batteries need to be charged to at least 14.2 volts (some up to 15.2, read the owners manual) to achieve a full charge. They need to be held at that level until they stop taking a charge (amps fall off close to zero). A multi-stage charger would be a great first step.
Solar is an excellent idea it seems for where you camp. Go for cheap at first. A second-hand 120w panel and a cheap $20 controller is all you need.
Check out the articles on dry camping in my blog (link in my signature, my first post was just after yours).
Happy travels!