As an update to my issue -- I did have to uninstall and reinstall FFXIV, but it did work fine after that -- I haven't had any glitches in my normal play. So, I'm going to assume my instance was an issue of something weird with the upgrade process and not the FFXIV client itself.

For reference, here's the basic machine stats:

Windows 7 >> Windows 10
GTX 970: 368.69