Logic says fuel issues but it also says fuel issues like insufficient delivery to the carb would NOT allow high speed/load running without missing and dying out until the load /speed was reduced.---I hear you saying rough running at idle and low speed after runing down the road normally.
A hot carburetor loses it's ability to provide an accurate idle mixture.
Also a look in the carburetor bowl may reveal some small particles that will plug or partially plug the low speed orifices---sometimes they move around and cause intermittant trouble.Look in that bowl.
