OK, so I replaced the power supply and SD card and problems appear to have gone away. It’s been running for 2 days now with no sad face reboots. Not sure if the problem was power supply (which never gave me any rainbow box warnings) or the USB install that was running. But it is stable once again.
I did accidentally get a UHS class 3 SD card instead of class 1, so we’ll see if that turns out to be a problem. So far the Pi2 seems to be handling the writes with amazing efficiency. Example: when I run Texturecache Maintenance Utility, my whole library can now be cached in less than 30 minutes, whereas it used to take 1 hour and 25 minutes on the USB install.
Thanks @DBMandrake for helping me troubleshoot the logs and narrow things down.