I am not positive, but I think Chrysler/Jeep got rid of the stupid system, beginning in 2008 when they switched over to 433 mhz sensors.....at least I hope so. To answer your questions though, yes, you'll probably have to bite the bullet or go to the stealer. If you purchase all the right stuff to fix it, remember it should work on any vehicle with a TPMS system....which is anything after 2006.
Regarding your left rear not showing, that may be another problem. The left rear does not have a TPMS pickup sensor/transmitter (trigger module) like the other 3 wheels. It recognizes the left rear by default....the other 3 with transmitters, so the one without has to be the left rear. Disconnecting the battery shouldn't have anything to do with this though. Usually, if you let the vehicle sit for a period of time, the message won't show up until after about 10-15 of driving. Having the continuous message is not a real problem, just a huge annoyance. It's something you can fix at your leisure, as long as you're able to get the pressures off the EVIC. Unless your mechanic has the proper equipment, and a good understanding of this stupid system, I doubt if they'd be able to help much. I know my tire place is pretty knowledgeable, and they were clueless on this system, and none of their manuals said anything about it. Also, IMO, if you're going to switch a couple sensors, I'd recommend you do them all at once. That way you shouldn't have to worry or do this again, maybe as long as you own this vehicle. Batteries are good for up to 10 years. Here's some of the info. we've talked about, copied from the FSM:
The wheel sensor ID’s and the location of each sensor (e.g. Left Front, Right Front etc.) are stored in the WCM non-volatile memory during the initial Manufacturing Plant Process, or during a service procedure, as required.
Transponders located in three of the four wheel wells of the vehicle to provide the Wireless Control Module (WCM) commonly referred to as the Sentry Key Remote Entry Module (SRKEEM) with the location of the tire pressure sensors on the vehicle. The transponders are located in the left front, right front and right rear wheel wells. A fourth transponder is not necessary in the remaining wheel well due to the process-of-elimination theory. Once the system knows the location of the first three sensors it assumes the location of the fourth tire pressure sensor is in the left rear tire.