tx....,
OK. It was pumps that suggested the pamcopete Chrysler regulator mod. I was all hung up on your idea to switch the tiny battery in and out, but you can probably run a small battery now with the voltage being properly regulated, others have done so successfully.
The trick to not frying a tiny battery is to never let the battery voltage get down to 10.5 or below, because then it will start drawing more current than it is rated for to recharge. I would even go so far as to suggest that you trickle charge the tiny battery over night....every night. Just wire up one of those 2 conductor trailer connectors to the battery so it is convenient to plug the charger in every night.