Couple questions

With the carb acting like that in the heat, it sounds like a lack of gasoline getting into the cylinders. How well do you know carbs? As in can you rebuild it. The fun out idea is a good one to possibly help. The insides probably, more than likely have varnish constricting the passage ways. This creating a lean condition that is amplified when hot.

Did you tinker with anything?
How’s many turns out is the idle screw?
You can try a half or full rotation out to allow more fuel through the carb at idle.

Between the idle screw rotation and the gum out, you should be able to get somewhere. It may only be inches needed for the full foot distance but some is better than none. It’s a place to start.

Nice ride.