I think I've found the issue, and fixed. VERY ODDLY, it wasn't an IE or antivirus problem, but a Steam problem.

I noticed that some people were saying that the Heavensward (which I own), was an extra 16GB d/l, after the initial 10GB d/l.

Apparently, if a FFXIV update went sideways, and you tried to fix it through Steam, it screw up the whole thing.

So I unchecked the DLC in the Steam properties, restarted Steam, re-installed FFXIV, with the DLC still unchecked. This fixed the initial boot error, and after logging in, I was informed I needed to download Heavensward, which had never popped up before. I installed the DLC, and all of a sudden, I was in business.

Game has been working two days in a row now.