It sounds like your fuel pump could be vapor locking. Modern gasolines have low boiling points which work fine with EFI. For carbureted vehicles, if the fuel pump becomes hot enough, boiling fuel will prevent the fuel pump from moving liquid fuel to the carburetor. Percolation in the carburetor will cause the engine to run rough from the added richness of boiling fuel and could cause it to stall from flooding. I would consider adding a solenoid-type electric pump at the fuel tank that you can run when necessary. See
Vapor Lock.
I would also add an insulating carb spacer to keep the carburetor cooler and make sure that the manifold heat control valve is lubed and working properly. The heat control valve replaces the heat absorbed by vaporizing gasoline in the intake manifold and helps the engine run better even in hot weather. See
Intake Manifold Heat.
Carry a gallon of water with you. If it stalls next time, try pouring cold water over the fuel pump.
YouTube: Fuel Boiling at Hot Pump