Remarkably, my radio has been working for over a week now. I use to always leave the radio tuned to FM when I let it sit overnight so I didn't have to deal with the Sirius not loading fiasco. A couple of weeks back I called Sirius and told them to cancel the service, since I wasn't going to pay the $26.95/month for something that didn't work.
After much back and forth, they finally came up with a $5/month deal and sent a refresh signal to the radio. I've been letting it sit overnight tuned to Sirius and it hasn't locked up several days now. Maybe it's just a coincidence, but before the signal refresh, I had about a 30% chance of the radio working after sitting overnight and about a 50/50 chance of the radio freezing up if dared to tune to Sirius after driving for a while.
Maybe FCA snuck in an update without me knowing it. I never saw any message about an update on the radio itself.