So.. the Chrysler rep "looked at" my Jeep today. And his answer?
"Everything is in normal operation with your Jeep"
So, I calmly picked up the Jeep and decided to test it myself again, just for the hell of it. I rolled down the passenger window, set the A/C to auto "LO", and shut the vehicle off. Remote started it, and....
HOLY crap it blows cold air out the vents!!
So, still not fully convinced, I drove it home and parked it in my driveway for roughly 30 minutes (plenty of time for it to heat up inside as it was 105 degrees outside)
Performed the exact same procedure, and ONLY hot air came out of the vents. I let the vehicle remote idle for roughly 7 minutes, hoping it would change. It did not. Once I entered the vehicle and pressed the start button as usual, the air became cold again.
What this means for me anyway, is that the problem is completely intermittent and changes as it pleases. This has led the local dealer to believe that I am completely crazy, and that they still see no problem with the Jeep.
My only solution as already said, is to wait until the software update comes and visit another dealer to request it. We shall see, I guess.
Sorry for somewhat redundant posts guys. Just wanted to share my intermittent frustration.