yeah the regulator usually only puts out 1 to two amps... kind of a trickle charge... while running, but increased with more power load.
Good luck on your set up, maybe them gremlins will pack up and move out.
No radiator here, air cooled... 14.5 amp charging system.
Deka batteries are top shelf, top of the line in batteries.
I'd really check your voltage at the battery while running at idle and high speed. Most SxS shouldn't be above 15VDC at Full RPM... any higher than that could be an issue with the voltage regulator.
What brand of battery ya using? I've been using Yuasa batteries (Kawasakie OEM), i get at least 5 years out of one... $60 from the kawi dealer.
you can also use a Lawn and Garden battery, provided it fits in the physical space. CCA is what you want.
Have you checked your charging voltage to be sure you aren't cooking the battery?
i would pull the valve cover and check the valve clearance .. if there is a flat cam lobe, the valve clearance will be excess... unless this uses a Over head cam engine.
In Lou'sana,,, i bet it's the humidity....
but just think, if you go all electric you can be like a tesla owner and carry a Honda generator in your bed. Or my electrical gremlins hopped over to your machines.