Limit the amps to whatever that battery recommeds.
That's the problem though... I can't limit the amps the alternator will put out. The only way is to turn on the headlights and fan to eat up some of the alternator's capacity.
What are you doing mining?
I started doing this in 2008 digging a pond. Since I finished the pond in 2010 I kept moving dirt for a variety of reasons having to do with trail maintenance, gardening, planting trees, cat litter. I'm basically still a kid in a sandbox with excavator and dump truck lol
At some point during your digging and driving cycle you need to stop everything for a half hour at least let the batteries rest
I usually do. I take a break for ME to rest mostly

You could have a battery with 11 volts start your ATV just fine.
It's between 12 and 12.3 now and it starts with a lot of power. The engine fires instantly. Not sure about 11 volts though. The engine is high compression and I have ovate valve springs which are crazy stiff.
You may need to switch to a true deep cycle battery or at least a deep cycle marine battery either way sounds like you definitely need a bigger battery.
I totally agree with you and wish I could find a true deep cycle marine battery that's small enough to fit. I don't think I can squeeze in anything bigger than U1. But U1 is pretty big for an ATV battery.