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Weak fuel pump would be my first thought. Not a lot of money or hassle to replace if you don't know the history of it.
Do you hear hissing if you loosen the fuel tank cap once the symptoms occur? How many lines connect to the fuel pump? Check fuel pump vacuum (draw), output pressure and delivery volume. Inspect the condition of all of the rubber fuel hoses at the tank and fuel pump. Verify that none of the fuel lines are in close proximity to the exhaust or other source of high heat. Replace the fuel filter(s).
Have you verified that none of the rubber lines are kinked or perforated? Loosen the tank fill cap the next time symptoms occur to make sure the tank is properly vented through the vapor canister and not developing a vacuum. With the fuel cap removed, try blowing <20 PSI of regulated air through the 1/4" return line leading back to the tank from the pump to verify the line isn't kinked or otherwise restricted - the return line exists to cool the fuel pump and limit vapor lock through a constant flow of fuel. Have you checked fuel pump volume? It should pump ~1 qt in 20 seconds of cranking. What were the draw and pressure measurements? Recheck the inlet filter in the carburetor to make sure it hasn't restricted and isn't installed backwards.