You could just buy a portable battery charger in any auto-parts store and begin using it to charge your batteries from the Hondas for the rest of the trip. You can pick up these inexpensive little battery chargers for maybe around $35-$55.
It appears that your converter might be the problem. Just turn it off during battery charging and use the portable battery charger instead for battery charging during the rest of your trip. You probably could even leave the converter still on during use of the little charger, as this won't hurt the charger or the converter .... and having both on just might stop the generator surging without having to hassle with turning off only the converter while using the new portable charger.
It wouldn't hurt to always carry this portable charger along, anyway, as a converter backup even after your converter is fixed later. We now carry a small inexpensive charger along for backup to our converter as a battery charger ... as I've experienced a strange converter failure in the past.