I had this with a Honda 125 once, turned out to be a duff rectifier, though Honda 125s then at least didn't have AC direct headlights, which should not affect anything else in the rest of your electrics.
Try running with the the half of the alternator that charges the DC side disconnected, possibly the reg/rectifier too, but with a fully-charged battery. If I remember correctly your bike is 2003/4, plenty of time for the OEM reg/rectifier to go t*ts-up since then.
I'm re-wiring an Electra-X soon, bring it round if you need to!
A.