If you have to hold your foot flat to the floor to get it started, then it HAS to be related to fuel flow. That points back to fuel lines/pump/SCV/pressure sender. It won't be a restriction on the inlet, because that would have the opposite effect to what you're experiencing (it would make it hard to get revs).
It might be the rail sensor not reading properly, and you'd notice that as either a distinct lack of black smoke (where you'd expect some) or an excess of smoke. A dirty or sticking SCV might cause some trouble but that's also usually the opposite of what you're experiencing (can't rev, but idles fine).
I'm just wondering if there's an air leak on the fuel line between the filter and the pump. If there is, at low fuel rates the proportion of air entering the line relative to the fuel being used is high, causing the actual amount of fuel in the chamber to be reduced which will cause it to stall. It will also cause it to be difficult to start unless you prime it first (try that?). At higher flow rates, the proportion of air entering the line will be less so performance will seem almost normal.