milleniumtree, you might be on to something with the EOC.
I had the same problem on my bike, I have to basically manage the headlight usage now and I bumped up the charge circuit so it charges more when the engine IS running. Still it gets a little low at times (tiny bike battery).
I also use trolling motor batteries in my small cars, just shoehorn them in and adapt, whatever
They seem to provide adequate starting power and don't mind being depleted nearly as much as a standard starting battery.