SOUNDS LIKE VAPOR LOCK. Modern fuel evaporates EXTREMELY easy, and the mechanical pump puts it under a vacuum. You likely have 3 PSI fuel pressure or less once its hot as soon as you open the throttle. What kind of electric pusher, and where is it mounted? Is there a filter anywhere before the mechanical pump?

You really need to measure the pressure with a gauge. My car on fuel pretty local to you would drop to 3 psi as soon as you cracked the throttle once hot. It was an animal cold. I spent a long time chasing my tail between the fuel pressure and crappy Thrush mufflers with a combo that should have made 500 HP easily until I mounted a gauge on the cowl. Once both of these were fixed it will bury your head into the head rest when it gets traction in 1st or 2nd gear (rare now, only on slicks). The car didn't nose over, or act like it suddenly ran out of fuel. In fact it didn't really seem like it was vapor locking, except for the fact that sometimes when really heat soaked it would act like it wanted to stall.

Can you get it to run at all when its hot and dies? Does it crank normal? What temperature does it run at?

You can run a compression test cold, then run it warm. If the engine cranks easy and compression is the same or higher it has nothing to do with piston to wall clearance or ring seal.

You should verify timing, but that's not your problem. Maybe the coil, or pertronix unit if you are running that.

If Nick built that engine I really doubt there was an issue with PTW. If anything mechanical I would suspect it might have an intake sealing issue that starts leaking once hot. You had the engine part to hone it but did not check the lash when you put the valve train back together? Check the lash, is it a solid cam or hydro?