Couple of things.
Your pump is either ingesting things, or it's inlet is being blocked.
Normally, there is no regular filter inline between the fuel pump and the tank. There is a screen inside the tank, and a check valve in the pump.
If your screen gets clogged, your car will starve (and make funny noises as it tries and tries to pump fuel. Same thing if your check valve gets clogged. Easy to check one of your old pumps. Take off the four screws holding the inlet port to the pump. There is a steel ball that prevents the fuel from running back into the tank. Check for rust and trash. All clean? No pitting on the ball? Great. The problem is in your tank.
Some may tell you to force air back into your tank, to clear the screen. Tempting, but don't do it. It will just return. Instead, have your tank removed, cleaned, and sealed.
If desired, you can add a small filter inline b/t the tank and the pump. If small amounts of trash are gumming up your pump, this should stop it. Just remember to change it along with your other filter.
If your electrical system is fine, then it has to be a fuel problem.