Ok, to recap, your issue is hard starting, followed by 15-20 minutes of bogging and lagging on acceleration, and when you pull the plug, it is covered in soot. Am I correct?
If so you have a rich condition, as stated above. The following checks have been done or made: Carb is clean and free of any debris, air filter is not clogged, all vacuum lines are routed properly to and from the carb and crankcase, spark plug is in like new condition, and a proper replacement plug??, verified coil and CDI connections and has good spark??, verified proper valve lash, and verified the choke works. Let me know if I missed something....
This leads me to 3 possible scenarios, the least likely would be low compression, but I think you said it runs ok after 15-20 minutes?? If so, unlikely, although a compression test would rule it out completely, and let you know exactly the condition of the engine. Scenario 2: plugged or restricted exhaust, you could rule it out by unbolting the head pipe and running it, if it clears up, gut that badboy, although still rather unlikely, unless it was burning oil at some point. Scenario 3: my personal thoughts, the pilot screw is backed out too far, letting too much fuel in. These GY6 carbs that have the mixture screw on the engine side of the butterfly, regulate the fuel, instead of air, like most other small engine carbs with the screw on the filter side of the butterfly. Screw it in a turn or so and see if anything changes. I had a similar issue with mine, and once I got it close, it seemed to fire right up and run ok, except at wide open, or if you let off and punched it again, which I think was the needle/main jet( I bumped it 1 setting on the rich side for the intake).
I hope this helps
