HiCustomer welcome to Just Answer!.
It's sounding an awful lot like a PCM problem, Josh... whether it's a situation internal to the controller or an external short is hard to say at this point. I see that you've checked your 5v feeds but I have to wonder if you found 'em all. The 5v goes to MAP, TPS, cam and crank sensors in this year and shorting of the 5v will take the PCM down instantly. If you've checked the circuit while the engine was down, forgive the reminder... The crank sensor is the most common cause for shutting the PCM down in these years when it shorts and sucks the 5v dry.
Aside from that, you'll just have a few powers and grounds to check. If the 5v isn't shorted and your have your needed powers and grounds, it leaves nothing but the PCM.
Connector 1 (C1, black/ black) of the PCM has four pins to check.
Pin 2... fused ignition switch output (hot only with key in run or start position). This is the wakeup call.
Pin 22... battery positive, hot at all time.
Pins 31 and 32 are both power grounds.
Pin 17 is your 5v supply and can be checked here or at the engine (orange wire).
C2 (center connector, white/ black) shows a 5v supply at pin 31, but I think it's only used on the 3.9/ 5.9 engines for transmission governor pressure sensor. My book doesn't say it isn't used on the 4.7 but I discount the possibility somewhat. Regardless, if the voltage source leaves the PCM and is shorted somewhere even though it isn't used it could be a problem.
C3 is mostly just driver circuits and besides the bus wire (Pin 30) won't have a great deal of interest to us here.
But speaking of the bus... If you catch the engine in its non-running state, you might try unplugging the C3 connector (grey/ black) to see if communication with other systems return. The PCI bus is a single-wire system that can be taken down by a single problem source, but if the problem is removed it will likely just pop right back up. Your ABS code for VIN mismatch is also consistent with a PCM that has been unconscious... when that happens the PCM can't broadcast its VIN to the ABS and it comes up as a mismatch even though it really hadn't SEEN anything.
Well, good luck breaking the thing! It's always good to have a positive diagnosis, but if you can confirm just these few things, I believe you will be replacing the PCM. It's hard to tell at this point whether the left bank upstream 02 heater problem is related to the PCM or not, but it won't have any bearing on the engine stalling out or lost communications. You might get lucky and have both problems solved with the same box.
Write back if you have any questions.