Fuel problem...need help

The worn down fuel pump rod is a really good suggestion, as I have seen that happen before.
Also one might consider replacing the rubber lines with EFI hose.
It's a lot tougher and todays alcohol mixed fuels don't affect it near as bad.

Taking the fuel cap off after it quits and hearing a long WHOOSH is a clue to no venting, which can override the fuel pump suction.