If you have narrowed the issue down to HDD stuttering you can mitigate some of that (not all of it) by nuking your preferences. It works for all kinds of HDD related stuttering.

In your Documents / My Games folder there will be a Final Fantasy XIV folder. Inside that is a bunch of stuff. Create a folder on your desktop, and remove everything in the folder into the temp folder on your desktop. Once that is done, move only your user folder back in to the FF folder, and run the game. See if that helps.