Here's the thing; I'd like to try to use small lithium-ion batteries for this; they weigh a ton less and are significantly smaller. The caveat is that if they're mishandled they tend to smoke and occasionally catch fire; the idea is to take the unregulated DC out of a full-wave rectifier with a capacitor on it, use a switching converter to get exactly the voltage the battery wants to see, and then another one to get exactly 12V for accessories. Apparently the existing TOMOS regulator is linear, so it just burns extra voltage instead of switching it.
Here's a link to switching vs linear regulators: https://www.renesas.com/us/en/products/power-management/linear-vs-switching-regulators.html
The gist of it is that a linear regulator is basically an adjustable resistor, so it gives you the voltage you want by burning the excess as heat; a switching regulator lets you go to a higher or lower voltage than what you have, and tends to be 90-98 percent efficient. On a system like a moped, where I only have 75-80 watts to work with and no ability to make more, linear regulators don't make much sense.
As far as why I'm looking at doing this, it's mostly an engineering challenge for fun; I'm trying to learn circuit board layout and a few other things, and designing something that I can use that other people might like strikes me as a good learning project.