I think with solar backup super caps would work. There are many videos floating around YouTube with people running power tools, starting bikes, and small cars with super cap packages. I think the risk is that if for some reason it doesn't start the first time, the caps drain themselves enough to not have a second chance.

Anyway, I'll have to bow out because I don't know anything about this. I run my little dirt bike (with no kick starter) with an 18Ah battery I got for like $30; and I can't even keep that bike running.