This sounds alot like what is happening, and it's never been repaired.

Make : FORD Model : F150 Year : 2004
Manufacturer : FORD MOTOR COMPANY
Service Bulletin Num : 05417 Date of Bulletin: MAR 07, 2005
NHTSA Item Number: 10014666
Component: ENGINE AND ENGINE COOLING:EXHAUST SYSTEM:EMISSION CONTROL:GAS RECIRCULATION VALVE [EGR VALVE]
Summary:
INTERMITTENT ROUGH IDLE - NON-COMMANDED EGR [EXHAUST GAS RECIRCULATION VALVE) FLOW. *TT

Where is this? Top of manifold or valve cover? I've replaced them before on my 96 but the 2004 is quite a bit different. On monitor I had a pretty steady fuel pressure psi of 39-40 lbs. It's a start I guess...