Getting the little passage ways and air bleeds clean on a carb is almost impossible unless you soak the body overnight in gallon of carb cleaner/ I mean immerse it totally, also double check the rubber intake tube that goes between the carb and head, if it sucks air through any cracks in the rubber it can cause it to die.
Carb has good fuel flow will recheck rubber intake tube. I took it apart clean it real good look like new inside. It will run ten minutes when I ride it and stop it shuts off cranks right back up.
If it were an ignition problem I doubt it would fire back up immediately, only way I see that happening is if the plug wire were grounding out against something intermittently, I know I forgot to tighten the clamp on the rubber intake boot on a four wheeler I had, and whenever I gunned it , it would pull the boot slightly off the carb, allowing it to suck air, and quit.
I have a Honda Recon. It would run fine as long as I gave it a little throttle. It wouldn't idle at all but would fire back up as soon as it shut off. I replaced the carb and all is well.
I'd bring a new plug and swap it out first before I took the carb back off. There really isn't any small passages in this carb to get gunked up. You've only got three circuits to clean and all jets and nozzles are fairly large on this carb.
I have a 1999 300. I bought a whole new carb off amazon for $35 and once installed it worked perfect. If it takes too long to figure it out a new carb is cheap!