Just to clear up the marketing jazz from the drill companies. Some use the max voltage of the cells in the batteries, while others use the normal/neutral voltage. Generally Max voltage for a LI-Ion is 4-4.2v, normal voltage is 3.6-3.7v. So a 3 series battery would be 3x4.2v= 12.6v which is the normal/neutral voltage of the Lead Acid style battery these atv's were designed for (max is somewhere around 13.5-14.5v). A prime example of the marketing talk is a 5 series battery, 5* 3.6v = 18v, just like a Milwalkie 18v drill battery. 4.1v * 5 = 20.5v, aka Dewalt 20v batteries. There's no difference, but the Dewalt appears to be higher voltage.
That's kind of the same logic with car amps today vs long ago. When I was a kid a 400w amp was pretty huge. now there's 1600w amps, but that's the peak output. The old ones were rated in RMS, basically continuous output. The 1600w one I'm using for an example is 400W RMS.
Anyway, liability is the #1 issue for a manufacture to make these batteries. I wouldn't touch them for my business because of that fact. For DIY, drill batteries would probably be the best source since they have a solid case and atleast a discharge protection circuit and under voltage protection circuit inside of them. I'm not sure if the charge controller is in the batteries or part of the charger. If it's in the batteries, then they should charge while riding, if not, you'd have to start the machine and disconnect it so it doesn't over charge (fire hazard). A large 18v drill battery like 5ah should have enough of a discharge spec to start a 3 wheeler I'd think, but the problem is, 18v Is a bit more than what the starter would be expecting. Probably wouldn't hurt anything as long as excessive cranking is never needed (heat kills the motor in the case of over voltage, so short bursts are fine, long hard cranking is bad). Ideally you'd want a Li-Ion 10.8-12.6v battery, maybe two in parallel.
Also fun fact, drill batteries are special made, same with E-cig batteries. Generally their discharge rating is 20C-40C, while typical laptop batteries are 1C-2C. Been a while since I've read about the discharge ratings, but if I recall correctly, 1c = 1x capacity, so a 2500mah (2.5ah) cell can discharge at an average of around 2.5 amps. 20C would be 20x that, or 50 amps. The "C" rating system is more of a length of time for discharge, so the rating is more of an average instead of like CCA being a peak rating I think. Here's a good write up on the rating system.
mit.edu/evt/summary_battery_specifications.pdf
Down side to the drill batteries is getting the connector to hook up to the battery and having a large enough wire to handle the current for the starter load.