The symptoms sound like the electric (and probably the mechanical) fuel pump are sucking air somewhere between them and the fuel pickup. This could be a pin hole in a steel line (I have found rust holes before) or a cracked rubber line either between the pump and the tank, or even inside the tank. They can be hard to find. If the problem is obvious while the car is stationary you could pup a line from the inlet side of the electric pump directly into a gas can. If that solves the symptom, you have determined the cause and just need to locate it. I am a farm boy who worked as a professional mechanic for many years (before and after the prevalence of fuel injection).