There are just two wires to the IAC valve, correct? I think that is a PWM system, at about 300Hz. You should be able to get a meaningful DC voltage reading across those wires. Compare what it is doing when it first starts and runs as opposed to when it begins to run rough; we may get some hints from that.
I went back and browsed this thread. Was the "high MAP" issue ever resolved? What about other things like moisture in the manifold? I was really looking to review live-data, but the photos of your scanner screens just were too small/blurry for me to want to bother with.
I, too, suspect this isn't a problem with the IAC itself, but is a problem with some other sensor that the PCM uses to conclude there should even be an attempt to control idle. MAF/MAP, VSS, TP, ECT, trans gear, and RPM are all generally used to determine if the engine is at "idle".
If the IAC drive signal goes away, or stops varying, when the engine starts running rough, that is a hint the PCM is not invoking idle control.
Please recap what the present symptoms are; as well as compression and FP readings.
I would also put a timing light on it, see if timing is dancing around differently when the engine is idling good/bad. And put the light on each plug, see if any are winking out.
Have you checked the injectors for flow-rate and spray pattern? At least, check that they are all the same (correct!) P/N.
My perception is this beast came to you with a lot of "unknowns", so I guess I am saying that we should "regroup" here...