Well, I'm happy to report I've solved the problem. I still don't quite understand how or why it was happening, but here's what I discovered. In my start bar, my sound shows as speakers unmuted. In my sound settings, it also showed as speakers unmuted. However, in my ADVANCED sound settings, it showed FFXIV muted. I have never gone there or changed it to mute... but... well, there you have it. So, if this happens again, I know where to look. In the meantime, I have my game sound back!