How do I get the ignition cylinder out without the key?

Easiest solution is to get a complete used ignition switch / cylinder from a salvage yard. You'll need a T20 tamper-proof Torx screwdriver or socket insert to remove it and the steering wheel covers. Check for heat damage to the switch terminals and the connector. It's real common for two in the middle of the connector to be melted or black from overheating. Find a different one if you see that.

There's three different lock cylinder designs. The difference is in the shape of the cam on the end that engages with the switch. The cylinder design has to match the switch design, but as an assembly, the three different designs can be used on all applications that use that type of ignition switch. Jeeps came with a design that's different from the front-wheel-drive cars and minivans, but you can use a similar switch from any application as long as you take the lock cylinder and keys with it.

Once you have the replacement switch, its cylinder can be recoded by any dealer's parts department people, but you have to have the original key if you want it to match the door cylinders. With no original keys, you could instead have the door and lift gate cylinders recoded to match the new key. If you elect to not do that, you'll have to be careful to never lock the doors.

All of this can be avoided by having new keys cut at the dealership. They can get the key codes from Chrysler.