John,
I would be concerned if you only replaced the converter that the wire diameter (likely too small) between the new converter and battery would still limit the charging.
Could you bring along a second fully charged battery and just swap when the first one gets low? Then, when the second battery gets low, put the batteries in parallel and charge both at the same time with your stand alone battery charger and generator. The charging wouldn't be perfect, but it would minimize generator run time and your outlay would just be the cost of a second battery, enough jumper cable to complete the parallel connections, and some time to fuss with it.
Oh yea. If your existing battery is older and/or hasn't been maintained as well as you maybe intended, it probably would be a good idea to replace it as well.
Hope you have a campout,
Steve