I had a '71 LTD with a similar problem. I had replaced the fuel pump and the notorious Ford fuel filter -- the one that screwed into the front of the carburetor -- to no avail.
I went to the local parts store, the one where the guys behind the counter actually worked on stuff and knew what the hell they were talking about. While I was standing in line to talk to my buddy Dave (who always had the best advice), I listened to a guy describing a problem with his Ford Country Squire wagon that sounded exactly like my problem. Dave told the guy that Ford puts a filter on the pickup tube inside the gas tank on that model. I knew instantly that my problem was the same.
I jacked up the car, crawled underneath, and opened up the front of the tank, where the fuel gauge float and the pickup line go in. I pulled the business out, and sure enough, there was a bag-type screen filter on the end of the pickup tube. I slid that filter off the tube and threw it away. Then I put the whole business back together, and I never had a fuel feed problem with that car again.