Thanks. You've done everything right to this point.
I can't tell whether it's they key's fault, the lock cylinder or a combination. I do have a few suggestions that might get you going, though.
If you haven't already done so, try inserting your keys in its other position. Wiggle it and such as you had been doing. Apply turning pressure while moving the key slightly in and out, up and down. Imagine trying to pick a lock (with your own key).
Since it's not a SKIM key you have more options. Look carefully at the key at full-insertion. Does it look like it's gone in as far as it should? Sometimes a tumbler will prevent full insertion so your key won't line up with the tumblers properly. You can try tapping it into the cylinder lightly with a small hammer or the like. The vibration from the strikes might be enough to rattle the balky part into submission, where ever it is.
If that doesn't work, remove your column shroud around the ignition area. I don't recall whether it uses Phillips or Torx screws. If it's Torx, it will be a #20.
An open shroud area will give you another use for the hammer. You have access to the sides of the cylinder now, which will set up a different vibration wave when shocked by the hammer. I'd recommend a smaller tool here, something that has little striking power, but will still rattle the part. An open-end wrench, jeweler's hammer... the like.
If you still have problems, you might try putting a hair dryer or heat gun on the lock. It appeared to work better in warm weather (I'm guessing).
Once you get it to turn, don't assume it will ever work again. Either drive it to a repair facility or remove the cylinder yourself.
Getting it to turn to the ON position is required for clean removal. Once it's turned on, look for a small shiny metal tab. This will be located a bit into the actual column portion. It's used to hold the lock in place. Push this tab in while pulling out with the key. The whole thing should pull right out. You can then use a large screwdriver to operate the ignition switch, just like it had been stolen.
Your local Chrysler/ Dodge/ Jeep store can code a new cylinder for you and make sure it works OK with your keys.
You might even have them cut you a new key using the factory archives. With proof of ownership the Parts people can pull up your key code from the original build information using only your VIN. The key they cut should be 100% accurate and might even work properly in your original lock cylinder. A typical charge for cutting a key this way is $10 or less.
That should about do it. I realize there will be no dealers open today, so your options are limited right now.
Write back if I haven't confused you enough!