I'm still blown away by how small the battery is for the rated capacity. It's really small. If the third wire is just for a thermistor (overheat protection for charging) then a 2-wire could be used by just swapping plugs. I would only consider that as an option if I can find the correct sized packs from Asia, where they would be $2-3 each.

...or just 3D print a new housing and put a 2,000mAh in there. Would run for days.