The leaking screw wouldn't cause the problem. All it did was act as another tiny little tank vent. More likely it was the few gallons of gas in the tank were not enough to completely cover the pick up screen so the pump was sucking a mixture of air and gas. When driving this little amount of gas sloshed around making the problem worse as it left the pick up completely exposed util it sloshed back over it again.
Well at least now you know how far you might be able to travel before you start running out of gas. LOL
Like I said earlier - its the little things that drive you nuts, in this case too little fuel in the tank. Glad you didn't have a major problem to fix.
Mike