Tried getting a new SIM card from the store, and updating my phone to the newest official release.
For some reason, when there's no SIM, it appears to be fine. As soon as I install the SIM and it resets, it barely makes it to the home screen before it randomly shuts off and reboots.
Actually, I discovered the problem: it IS the WiFi connectivity. What's up with that? Can I do anything about it? I'd still like to have WiFi calling/access if I can.