I was trying to flash the new modem, but wasn't installing even though Odin reported success. I must've tried 5 or 6 times, and then it finally took. The only difference was that the last time I completely turned the phone off and manually started in Download mode (Power + Vol Down,) while all the previous times I was rebooting via CM11's "advanced reboot" dialog (power button -> Reboot -> Download). I guess something either in the ROM or the phone itself isn't properly starting when you reboot to Download mode from within the ROM.
TL;DR - power off your phone and manually boot into Download mode for proper Odin/Heimdall flashing.