Are you using an oem fuel pump or aftermarket ?

If replacing the fuel filter helps a lot, that still indicates fuel supply problems (marginal pressure) IMHO.

I'm having similar problems ('97 Zetec), just replaced the FP (this is the 3rd one).

Someone suggested looking into the fuel tank to check if the baffles (actually more like a spiral shaped maze) are OK. For me they look fine.

Tiv