Out of all the data you've posted, I really haven't seen any of the PIDs I would really be looking at for lean or rich codes. If you are limited to 4 PIDs, the ones I would be looking at would be STFT, LTFT, ENGINE LOAD, RPM/vehicle speed.
Until you can see your LTFTs go in to the 20% range you aren't in the problem area. I haven't see a Ford yet that will code in the teens. This is where freeze frame data can be so helpful. Right now you having to try this condition and that one to find the area. With FF you can see temp, speed, load, etc. 1/2 the battle is finding out when it's failing after that, then its "what hell is causing this"..
I haven't had a problem with the Taurus but the 4.0 Explorers had a plenum issue with gaskets and bolt and would only code after a cold soak (sat all night). After they warmed up, everything expanded, sealed and the trims would come in line for the rest of the day. So you'd think, I'll just look at the trims after a cold soak and that will tell me.....
That would be too easy.....
On Fords, part of their cold start strategy the is trims go high, real high for a little bit, which makes sense, this means the PCM is adding fuel which you want when it's cold so if you go that route you have to be real familiar with what normal high trims look like and what trims that are too high for too long and will set a code look like. Honestly in these cases where FF is pointing to a cold soak problem, I just smoke the manifold after it's sat all night. Its much quicker and more accurate (unless an installer does me a favor and warms the car up for me before I get there....that's always a fun phone call for the SA ).
So 1st I'm assuming you already followed HTs original advise and looked for the obvious leaks, looking at the PCV hose very carefully and making sure then snorkel was hooked up to the throttle body with no cracks or splits, no obvious exhaust leaks....the basics... If all the is done then you have to find the spot where the LTFTs go over 20% until you do that, you're in the wrong area and chasing ghosts......
I did see a TSB for the 4V 3.0 for an O ring problem on the intake but that is for the S engine not the U engine and IIRC you said you had the U.