I'd drain all the gas out of the tank, pull it, then flush and seal the tank.
Even if that's not the problem, it will be some day.. it's something that should be done with any vehicle 40+ years old IMO.
Since it actually starts and runs a few miles or so before it starts acting up, I wouldn't suspect a clogged fuel line, since if there was enough crud in the fuel line to stop the engine, it would probably run like [censored] from the get go.
Inline fuel filter between the pump and the carb is a must have, as well. If you don't already have one, get one.. if you've got one, replace it.
With a clean and sealed tank, a new fuel pump, and a fresh fuel filter in line between pump and carb you fuel system should be good to go.
You probably have crud floating around in the gas tank.. as gas is sucked out of the tank by the fuel pump, this crud collects and finally clogs the flow. When the engine is shut off, the crud floats away and flow is restored.
You said with the new fuel pump the problem actually got worse.. which makes sence. Increased suction would mean that crud gets sucked to the "clog point" faster.
Sounds like natures version of the old pingpong ball in the gas tank trick.
