This sounds like you’re getting there. You could prove this theory if you run it until it’s too hot and causes the issue then stop ( like there’s a choice) pop off the air filter and drop a capful of fuel very carefully down the carb (hot motor, careful careful) if it starts immediate then you’ll know for sure it’s a fuel supply issue. If it’s definitively a fuel supply issue it would be easy enough to pop the pump off quickly to see if indeed the pump rod is jammed its only two nuts and leave the fuel pipes all connected, and just wiggle the rod up and down. New pump usually means a new rod and possibly a new mount / guide thing that the rod slides up and down in. This could indeed be the main issue. Running this around in my head, I can’t see the rod seizing on its own as there is a bit of slack, not much but a bit. It’s possible that the rod is slightly bent perhaps? Or the pump stand / guide thing is expanding as it’s getting hot and gradually squeezing the rod until it can’t jiggle no more, which would indeed make it a bit of a pig to try and tune the motor so it may actually be running a bit hotter than it should and enhancing the issue. If it’s all new ish then theoretically it’ll all be a tad tight.
Ozziedog,,,,,,,,that ^^^ might be all baloney