Don't you love those driving episodes like this when your hear rate zooms and you're not sure if you're gonna make it home and its a coin toss if you will or call the flat bed?
Hopefully, Franks idea gets you back on the trail!
I'm thinking outside the bun here and have an idea your ignition switch is failing/faulty--the chimes and dash lights and stall die out are the drivers for this.
Ignition switches get a lot of abuse-hope you don't have 40 keys on the ring or a heavy pendant (HD or Alma Mater or similar) as the guts of the ignition switch (IS)aren't meant for that and do wear out over time.
Try this to 'see' if the IS is letting go:
Turn key to 'on' and then continue to 'start'
Just as things power up in the 'start' position, let the key return to 'on' (run) -NOTE: [Don't actually start the engine]
Here, what you need to look for is the activation of the various 'warning' lights (oil, brake, charging) as these will not be visible at key click one (on /run).
If these warning light 'activate' when you turn key to 'start' and then go out when you allow the key to revert to on/run, then your switch is faulty and all the above symptoms you dealt with can be expected.
I've heard of some using compressed air to clean the units as all that junk in our pockets (dust, thread, fuzz) can get wound around the keys and then placed in the switch inadvertently. I think there's a release tab for the key/cylinder on your Jeep which can be accessed from the 6 'clock position on the trim piece below the key on the steering wheel assembly if you want to start with cleaning that first.
Keep us posted! Bonne chance!
Here's a vid of how to swap out the old for a new IS. You'll need Torx bits.