if it were me i would just belt an alternator up to the lawn tractor
gear it right so that it will turn the alternator at about 3k rpm at just above idle
and use the reostat to provide crude regulation.
i doubt that engine will burn a half gallon per hour charging maybe 30-40amps
but do get a 100amp or larger unit if possible,, 30-40amps continuous on a large alternator will run forever without problems. and if you need more amps just throttle up the motor and crank up the reostat which is very acceptable for quick charging if you keep an eye on the batteries and don't overheat or overcharge them, which probably is not likely in an emergency situation and the batteries are pretty much drained anyway.
i don't think there is a car on the planet what will idle while producing charging current and use less fuel.
also i you botch the connections when it is dark and rainy or your tired you end up toasting the add on alternator on the tractor, something you can replace easily ourself, toast your car alternator or do other damage and you have an expensive repair and your on foot maybe,,, or maybe even a tow bill.
my vote is an add on to the garden tractor :)
bob g