Thanks for the reply, but still no good, at least with shutting the phone down. I let the SIM card sit out of the phone for those few minutes as well.
Now here's something interesting: I changed my preferred band setting (running CM11) to LTE/WCDMA, which supposedly is 4G LTE and 3G, respectively. So far, LTE has held. But my phone has been on the Global setting for the longest time, so I might just pay a visit to the VZ store on my way home from work tomorrow to see if I can beg them for a new SIM card, since I probably won't be able to get 2G/1G signal on this current setting. At least, I don't think I will. And it probably doesn't matter, as I'm usually around LTE, let alone 3G, coverage...
Edit: Nope, dropped to 1X after about 15 minutes of LTE. To VZ I go!