if you're still being dropped out in even in windowed mode your option is pretty much limited to using Valve's Steam overlay to run FFXIV in full-screen mode. I get dropped out constantly in windowed mode due to the Direct X error. With the steam overlay/full screen I only get dropped out when I'm stupid enough to accidentally hit alt-tab.

Choose to add non-valve game,
Set FFXIV to run in full-screen mode, and at the full screen resolution.

You'll have access to websites with the Steam overlay and not much else.