The way you describe it as chugging to a stop makes me think you should check for fuel in the oil.. when it's cold and before you start it check the level hasn't/isn't going up, and take the oil fill cap off and smell for fuel. That does happen. Other than that you should check the state of tune, how the spark plug is, replace it if necessary, adjust the valves, adjust the idle mixture and speed.. That might cure it and is the recommended starting point.. Then, if you bought a cheap timing light it would tell you if the spark was dying out after fifteen minutes if you still had the problem.. Or.. To eliminate the electronic part, any way you could borrow a buddiy's cdi unit, or that would be ok with you trying your's on his bike to see if it changed things.