2001 Mazda MPV engine stalls

When you press the accelerator, the van acts as if it is running out of gas. Jerking. Sputtering. Sometimes even stalling completely.

The mazda dealership service staff have replaced the mass air flow sensor (that was the code showing on their computer) as well as the fuel pump. They also drained the tank and cleaned. The engine does run better but it still has the same symptoms. Just not nearly as severe.

I have no idea what to do next. Is this something common with this vehicle? Any ideas on what to try? I have already laid out approx $1000 for it so far and it's still not right.