Too bad you do not have a way to test the fuel injectors? I got a set for my 04 GTP from Morad Auto parts in Ohio, they were used, but worked perfectly and not that expensive. Checking the O rings is ok, but if you have an injector that is not firing correctly that could cause a miss. If you have around 60 psi on the fuel rail and have done all you have stated and the code came up that would still tend to lead to some fuel issues as you have described. You can have the PCM flashed by GM, but I agree that the PCM cause is not the most likely possibility at this point.
I replaced BOTH the Cam Sensor and the Crankshaft Position sensor in my car. The Camshaft sensor was easier and seemed most likely at the time, but it did not fix the problem. Both sensors COULD have caused the problem I had, but it boiled down to the Crankshaft Position Sensor in my situation. The code that came up on your car was not the same issue as mine as I NEVER had a code come up at all.
Yes the Snap on Scanner is a lot of money, I would just have one put on the car to see what it says, I have done that in the past and even did it prior to changing the CPS, but no codes showed up on the Snap On Scanner at all, past or present codes. The main reason for changing the Cam sensor was HEAT affected issue. Your issue seems to be more COLD issue then heat. Both COULD cause it though I guess?
Sounds like you saturated the fuel system good with injector cleaner " Sea Foam and more " If the darn injectors are an issue just changing the o rings will not help unless you can see or smell fuel. if you have bad o rings you could see the fuel by the injectors. The injectors on a series III are longer and different than those out of an older 3800 motor.
Just for the heck of it I looked up GM 3.8 3800 Supercharged Fuel Injector P/N 12574393 L32
Item condition: Used set of 6 Price: $74.99 Plus shipping
With everything that I did to my car to try and find the problem I spent close to $ 300.00, that is with FREE Snap ON Scan and doing everything myself at no hours cost included. Yeah I have an extra Cam Sensor and an extra Fuel Pump laying around, but I feel it was not wasted money, just extra parts for later on.
You will find the problem and hopefully soon. Talking to a local GM dealer they said that they would not have been able to detect the issue I had with any of their equipment, just one of those process of elimination and reading things to finally find the issue.
If I was to bet on anything I would lay odds that the injectors or wiring is not right. The 3800 Series III is a Sequential Fuel Injection ( SFI ) motor not a Bank firing so even the wiring could cause issues also. Being as new as your car is, it is not likely to have wiring issues, still more likely some crap got in the fuel injectors and some are not firing correctly, " pulse width or pulse rate " . Still at this point it is much easier to GUESS then have proven FACT.