I will mention this, but I am sure you must have checked the water-fuel separator filter at the shut off valve. Since it recovers after a short period off, it really does sound like a fuel flow problem (or pressure). Sounds like the pressure and flow are ok for 20 min and then cannot keep up with the fuel demand. Especially since you are finding dirt in fuel system. Maybe from the take. Is the fuel bowl at the water separator not full of fuel when the problem starts? Maybe a restriction at the fuel tank outlet, if so.
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