I've determined that the issue is with my host. I now have 4 domains with them. Two older (my site I'm having problems with, and a backup) and two newer (one I made a couple months ago, and one made today for testing).
After -completely- deleting the entire PHP database and recreating it, completely deleting everything from the FTP and reinstalling wordpress... The two older domains exhibit the same issues. The two newer ones do not. At this point, there isn't much I can do that is within my control, so I just have to wait for them to get back to me.