The detail about it cutting out like a rev limiter before it died points hard at the coil rather than fueling. If it were the carb, dribbling gas in the cylinder usually gets at least a cough. While you wait on the coil, cleaning those earths and getting a battery in the circuit costs nothing and rules out the regulator spiking the CDI. A TMX30 is a big jump from stock, so I'd get it firing on the original carb first before swapping. Bone dry from sitting is one thing, but make sure the crank seals aren't dried out too.