CDI does to a point, but I believe it will either work or not. Blowing lights and the overheating of the hand warmers sounds more like a short.
The short could be sporatic. Try disconnecting the hand warmers and see if that fixes it, if not, do the same to the lights one at a time i.e. head light, tail light. Test your regulator and buy lots of bulbs
I had a short on an old Panther once and it took forever to find it, ended up re-wiring it, which is when I found the short, a small bare wire I couldn't see till I took it out.