Well, I used F() on a bunch of my strings, and callsToday[ 0 ] is now 0, the way it should be.
As for the PROGMEM, I'm reading about it now, and it seems wonderful, but also complicated. It's going to take me a while to learn this.
Maybe someone (if they're feeling extremely charitable) can send me some example code for converting my 3d char arrays to PROGMEM arrays?
I've googled it, and found some info, but to make sense of it all is going to be quite a task...