I hate to sound like a broken record, but it sounds like clogged fuel line to me (which has been my diagnosis for severel problems reported on BCF lately)
The residue in the tank, either tiny bits of rust or sometimes the tank liner itself if it has been treated with some sort of liner to prevent the rust problem and it is flaking off, anyw the residue is pulled to the clog point somewhere in the line and compressed to the point it won't flow fuel by the gas being pushed/sucked through the line by the fuel pump. Stop ofr a while, pressure goes away, silt loosens up, car runs for a while--then the same thing happens.
I would pull the float bowls and see if if looks clean in there, also the fuel line as it goes into first carb, and maybe as it goes into the pump as well, if you see a lot of little brwonish or whitish flakes this is probably your problem.
You can also disconnect the line at or near the carbs as soon as the problem occurs, turn on the ignition again and see if the gas is coming out OK (Drain it into a cup or something) should spurt out farily strong with each click of the pump.