From reading between the lines on your battery use, I'd suggest to buy two new 6v GC2 batteries and hook them up with fresh wire and new connectors. The 6V batteries will be more tolerant of your use and will last longer than another pair of Walmart Grp 24's. The 6V are about the same price, if bought at a discount outlet like Costco or Sam's.
After the new batteries are in, you should look at your charging regimen and figure out why you are not getting a full charge to the batteries. Usually, an owner drives a few hundred miles back from the campgrounds and calls it a day without knowing, fully, what state of charge his battery is at. The battery may be disconnected or it may be allowed to run to nothing from the parasitic loads and recharged when another use is anticipated. Using two batteries and changing them out when one gets low, only adds complexity.
You could try to equalize both of the Grp 24 batteries you have and then put them on a trickle charger for a few days. That may get some more use out of them but batteries are kind of like elephants, they have a long memory.
AFAIK, the 12V charger output of a Honda 1000 is about 8 amps. Your stock converter should be better than that by a factor of 4X.