Don't wanna go against the grain here, but I have had an outside fuel pump, in the tank area, for quite some time without any problems. Albeit the car has been sitting for several years now, but when I did have it running I can assure you that I played hard, hammering the gas many a time and without any stalling what-so-ever.
I am not trying to say that is not the problem, it most certainly could be. All I am saying is, it may not be the ONLY problem. If you have a good fuel pump, even outside the tank, and within parameters fuel pressure there may something else that is the nasty little culprit.
A buddy of mine recently found out the fuel pickup in the tank of his 70 Chevelle was bent in a "V" shape. The mechanic called him and said "I'm surprised it got gas at all". It didn't run bad before, he was having a gas gauge problem, that they thought was due to the sending unit. They replaced the pickup/sending unit and, voila, the car runs great.
I reread the thread and didn't see where you said you have had the tank down, the pick-up/sending unit out and checked for obstructions or damage. Sometimes the "sock" disintegrates and that crap will clog the pickup. Or there is some other problem not allowing the fuel to flow. Or the sock has rotted and sediment(dirt and other debris-as Marco said) has found its way into the pickup tube. Maybe disconnect the tube somewhere near the tank and blow air through the line backwards toward the tank to see if anything is dislodged.
Has the car sat for a long while? Is there any reason to think there is any kind of old gas sludge build up in the line that may have became loose and lodge itself somewhere else?
Another thing, is the fuel line run anywhere near the exhaust or any other heat source? I know you have tested the fuel pressure without the car running---cold check---and got a ZERO reading, but be sure that once you "think" you have it solved it may show up and throw you off. Just trying to cover all bridges here.
I, for one, am very curious as to what you find.
Good luck. These types of things can drive one nuts tryin to find the gremlin.
cheers, jer