That's a scooter, not a moped...no PEDals. Some ppl here are touchy about that.
You replaced a BUNCH of stuff. Are the symptoms still the same (as in actually the same, not a different but similar behavior)? Is there an intake pipe between the carb and the cylinder? Might be an air leak between carb/intake/cylinder. The carb controls and meters the air/fuel mixture that is making it to the combustion chamber. An air leak can act irregularly and cause a bunch of headaches with idling, seen it on snowmobiles, dirt bikes, lawn mowers..... could also be something loose. Bolts on the intake and exhaust tight? (Intake being more important than the exhaust). Gaskets good all around?
What does it act like at other throttle positions? My guess would be that you notice it less at WOT.