I think of ALL the problems, electrical are the worst possible ones.
Continuing with the short circuit, (I believe it's that, SOMEWHERE).
Pull your seat and start there, under the tank, then the handle bars switches.
I was thinking as I was out yesterday breaking in my Military about your hassles.
If, it was the regulator, wouldn't it blow a smaller bulb like a turn signal, speedo bulb before a heavier duty seal beam head light??
On my '04 Bullet, I had WEIRD electrical problems. I cure all of them by running a good ground wire from the battery to the engine, engine to frame and split it to the front and back of the bike. I tied ALL the lights, (and horn) into it and that seemed to cure it.
Maybe instead of power hitting ground, a intermittent ground causing a surge at the
?.
I concur with the carb junk problem.
Road speed isn't the issue, it's engine RPM, or better yet, throttle position, (which circuit are in in, pilot jet, needle, or main jet).
One of the first things I do when I get a bike is install a in line gas filter. Keeps "stuff out of the jets.
I also could have been a bit of water in the bowl. Add a tad bit of gas line anti freeze, and some carb cleaner into your tank.
The bike could also be running lean, then when it got ccccooooolllldddd, it needed more fuel to be happy and because it was lean to begin with, the problem only magifies.
Pull your plug and see if it's a nice golden brown.
I pulled mine yesterday, (it was @30 degrees here in Pa. in the AM), the plug was too clean, (granted it only has 65 miles), so I know it's lean to start with.
Again, don't get discouraged, take it one small step at a time, take nothing for granted.
This, like all advice given here, should be take with a grain of salt. Although many of us have had the similar problems, how each one of attack the problem, like anything is, a personal thing.- That's my disclaimer!
Good luck and keep us posted.
Joe
I ride, therefore I am!