Bishie, welcome to the forums, let's see if we can help with your troubleshooting dilemma. As you likely know by now, here are the DTC definitions for your trouble codes:
P0340—No camshaft signal at PCM
P1765—Transmission supply relay control circuit voltage at unexpected level
P1391—Intermittent loss of crankshaft or camshaft position sensor
P0531—Air conditioning refrigerant pressure sensor circuit
P0761—Shift solenoid stuck
C214C—Emissions management issue
P0301—#1 Cylinder misfire
While the persisting code is a shift solenoid stuck issue, there is more to this. First of all, I'm not into the philosophy that a DTC code means an immediate call for new parts—especially when you get a constellation of codes at one time and some never come back once cleared. This "global" kind of trouble codes, when it occurs suddenly (like after filling up with fuel or any other single event), can often point to a defective PCM. While a backfire through the intake can be a camshaft position or crankshaft position sensor issue, a variety of other problems can cause a backfire. A defective or malfunctioning PCM can make the entire powertrain and chassis system seem like it's packed with defective components.
I understand that you have tried to be logical with the information offered by the PCM/DTCs. Let's first take this back to the original problem and its starting point. You mention filling up with fuel to the brim. This could be an issue of bad or incorrect fuel or an emission system issue caused by over-fueling the system. It sounds like that initial trip home was in limp mode, which is often triggered by a defective O2 sensor. This is possible and could also relate to fuel quality or the type of fuel in the system. Any of these conclusions would encourage digging deeper or replacing parts.
You followed the logic, or illogic, of these thrown "diagnostic codes". (If the PCM is actually defective, the codes thrown do not represent parts failures but rather the inability of the PCM to interface, read or drive these devices.) The wide array of unrelated trouble codes points to a possible universal electronic problem and not a slough of mechanical parts that suddenly and mysteriously failed.
Think of the PCM like a motherboard in a PC computer. If the motherboard fails, all of the data and in-and-out information flow gets compromised. Although the PCM is supposed to interrogate itself, they often fail without a trace. If this were my Jeep, I would first unplug the PCM and check the connections for corrosion or damage, then carefully plug the connectors back into place to see if that corrects anything. If not, and if you have access to another PCM for this particular model, consider replacing the PCM or at least testing the vehicle with another PCM.
In your case, there's also much to be said about scanning the system with a Chrysler dealership DRB-III scan tool for OBD-II. The cost of a diagnostic check would be far less than the expense of needlessly replacing a laundry list of parts that could be erroneously showing up on the MIL as defective, some storing codes in the PCM. The PCM could very well be defective.
Caution: I did a quick look around the internet for a PCM price. They range from $450 to $600, presumably new as there was no core charge. This is quite expensive for experimenting and would likely be a part that cannot be returned unless defective. Find a much less costly solution if you can...One approach would be a recycling yard, the lowest priced used PCM you can find for your model, it can always be re-flashed, although again, that would call for the dealership DRB-III scan tool...A dealership scan is looking cheaper all the time!
This is a start...Get back to us with your next step and any conclusions...Glad you joined the forums!