If you know somebody who has an ECM that you could try; however, your description sounds exactly like what mine did when my coil went out. It would run great for a few minutes (in the dead of winter) and then go straight to crap. It throws all the codes because it is experiencing those issues (due to little or no ignition).
Think about it, your O2 sensor pops a code because there is fuel in the exhaust that isn't burned... because it was never ignited.... because you aren't getting spark.
If you've got fuel pressure (which normally indicates that you're getting fuel), and you have compression, then you're probably not getting spark. Toss a spark plug test light on (you can get one for just a few dollars) and let your Jeep idle until the problem happens again. When it starts bucking, if you're getting no light or intermittant light, you'll at least be able to narrow it down to ignition.
And if I can be honored to speak on behalf of the chuckle heads, the picture of the girlfriend definitely doens't hurt.