Jim, what kind of fuel are you using? Is this an ethanol blend pump gas, or non-oxygenated pump gas, race gas, or? Your problem kind of sounds like a fuel boiling problem. Today's pump gas is designed for EFI systems rather than carburetors. In an EFI application, the fuel is pressurized right up to the injector at 45 psi or so, which raises the boiling point significantly. In a carb, once the fuel enters the float bowl it is no longer pressurized and will often boil. I've had fuel boiling in carbs when the outside temperature of the carburetor is only around 150 degrees as measured with one of those infrared thermometers.
If it is a fuel boiling problem, then the car is stumbling at the top end due to too much gas, rather than too little. Boiling fuel will foam out of the carb vents and flood the engine. Feels just like you are running out of gas.
Non-oxygenated fuel is better in terms of boiling point, and race gas is better yet. I think it might be worth putting five gallons of 110 octane leaded race gas in your car next time you are at the track, and see if you have the same problem. If you do, it would at least eliminate the fuel itself as a potential problem, and if you don't, then you can take steps to correct the issue with pump gas.