Unless there is a leak at the hose connections, the idle air control valve will not affect fuel mix. It just controls how much air bypasses the throttle plate. If it gets worn or dirty it will start to stick and you will get a jumpy or incorrect idle speed. If it gets too jumpy then the engine will run rough. You can remove it and attempt to clean it by flushing with carb cleaner or Varsol and allowing it to dry. You can also try using the OBD connector to run control function test #3 and exercise the idle control valve which sometimes helps unstick it (see this old post).

I didn't realize your FPR was that new. That does seem to put the O2 sensor, AMM and FPR more as equal suspects. Unless the new FPR is faulty then apart from a plugged vacuum line to the FPR, that really kinda squashes my theory. And I really thought it was a good theory. Busting open your frozen fuel rail fittings does seem a bit severe just to keep me happy. Measuring fuel pressure at a fitting before the FPR will really only tell you if the pump is providing enough pressure. If the pump was the problem I'd expect you'd have fuel starvation at high revs. Just for jokes, with the engine idling, pull the FPR vacuum line off the intake manifold, plug the fitting with your finger and suck on the end of the hose to simulate heavy vacuum. The fuel pressure should drop causing the engine idle to momentarily drop until the idle control system is able to adapt. Also, if you taste gas from the hose then the FPR has a diaphragm leak.

Just in case, I'm sure you know to clear the codes and watch for them to re-appear. It would be interesting to know if the codes are tripped with a cold vs. fully warmed engine as that may implicate the block temp sensor in all this. The O2 sensor isn't used until the ECU sees the engine is fully warmed.

I have another thought for air leaks with your B234F. I used to have problems with the spark plugs in my '89 B234F becoming loose until I learned to tighten the plugs to 20 ft-lbs (22 for a used plug) rather than the 18 ft-lb spec. Proper plug torque varies depending on wet/dry thread and whether the plug has a crush washer or not. Just for jokes, check that your plugs are tight and that there is no evidence of blow by in the plug recesses. If there is oil in the plug recesses then the valve cover gasket is leaking and the plugs and insulator boots can become contaminated and misfire.

To address your rough idling, I offer the following from my notes. Simple rough running shouldn't cause the fuel trim code. You probably know a lot of this, but I'll mention it anyway. B234F's run rough at idle if there are excessive engine deposits or if the throttle body isn't properly adjusted and kept scrupulously clean.

o Pull your plugs and check for excessive deposits or incorrect gap. Deposits accumulate easily with low rev, stop and go city driving. That would definitely affect rough running and it is most noticeable at idle with the B234F. One way to help prevent this is to stay out of overdrive in the city. I switched to a longer nose plug (NGK BPR6EVX platinums) in order to minimize combustion chamber deposits as I was doing a lot more low rpm city driving than highway driving. I was very happy with those plugs and a set lasted for ages.
o The injectors may be fouled at the tips which initially causes a poor spray pattern and ultimately leads to uneven fuel delivery. Perhaps the addition of a quality gas additive injector cleaner for a couple of tankfulls coupled with the some high revving mountain highway driving will make a big difference. One thing I have noticed and others have mentioned is that after using an injector cleaner additive, wait an extra tankfull or two then pull the plugs as they will likely need cleaning (or delay switching to a new set of plugs until after you've used the cleaner).
o B234F's seem more prone than most to spit up oil from the crankcase into the PCV system. This fouls the throttle body throat and as the problem progresses the air intake tube and vacuum lines get coated. The flametrap and PCV hoses need to be kept clean, especially the small hose off the top of the flame trap. I've often seen that hose and it's manifold fitting totally plugged. If necessary, ream the hose out with a straightened coat hanger with the end filed into a blade.
o When you clean the throttle body it's always best to remove it from the intake manifold and take it to the bench for a proper cleaning. Use carb cleaner or Varsol, a rag and something like a toothbrush. It's important to keep the outside edge of the throttle plate clean along with the area in the throat that surrounds it when closed. The vacuum orifices need to be clean so flush them out and blow clear with compressed air. If there was an accumulation of deposits near the holes inside the throat then the holes may need to be reamed clean. For tiny holes use a pin, for larger holes use a drill bit to carefully ream them out. Occasionally open up the brass fittings for a proper inspection and cleaning. You need to make sure the throttle body is properly adjusted. The procedure is fully documented in this old post. When re-installing the throttle body it's best to use a new gasket, but the old one will do in a pinch if it's not damaged, you keep the original orientation and the mating surfaces are kept clean.
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Dave -not to be confused with a real expert