Mine did exactly the same thing. Mine is a fresh rebuilt 45. I do have mine converted to 12 volts and an msd ignition with electronic dist, so that may help with the electrical question since mine did exactly the same thing, and it couldn't be farther from stock. Anyway go to Napa and buy a 1 gallon can of carb cleaner, the kind you dunk your carb in overnight. Once clean, blow every passageway out, and run a piece or wire from a mig welder through every hole you can find and reblow it with air. Then rebuild it with a rebuild kit. Not only did it totally fix the problem, it starts easier and runs at a lower rpm very smooth without the occasional pop thru the exhaust.
Hope it helps, and if it doesnt, at least you have a brand new clean carb (which can't hurt) and you can focus your attention on something else.