An update. I attempted a few things such as lowering the graphics settings further and further, those did not appear to assist. I used the 'restore settings default' option on the game launcher and for a little while things appeared to have been fixed, but they soon proved not to be so. I also ran other games that use DirectX so I can confirm the issue does not lay with DirectX itself, instead it lays with FFXIV somehow. The most recent crash not only froze my computer temporarily, but it caused 'System Interrupts' to rapidly fluxuate from high levels of CPU usage to none every few seconds. It took a bit of work and restarts to get my machine back in operating condition.

Some additional information for this, my graphics card is a Nvidia GeForce GTX 660, Driver Version 347.52. My rig has 8 Gig of RAM with an Intel Core i7-3770 CPU @ 3.40GHz. My OS is Windows 7 Home Premium