Flattening solved my problem.

I reinstalled Win 7. I had all current drivers and BIOS updates before. A few things come to mind after all this that could be the root cause.
  1. Newer video driver (Nvidia 580M SLI)
  2. Direct X
  3. Game controller driver (Logitech F710)
  4. Related to a game patch

This time I used all the most current drivers except Nvidia where I went with 314.22 that people on ffxiv forums were saying was stable.

For the controller I had trouble reinstalling it and had to use a Microsoft driver to get it to work. Then had same crashing problems again in game. So I wonder if it was the problem. This was caused by having the controller already plugged in when I installed the driver. Don't do this. The only way I could figure out to fix was wiping the machine a 2nd time. With this install game worked fine.

On Direct X I had used the most recent from the Web. This time I'm just using the one that came with the game.

So again for me wiping and a good clean install of everything seems to have worked. Right now the most likely source of issue was newer video driver, Direct X, or game controller driver and maybe related to a game patch. I've been able to play game well now for a few days on high laptop settings with no crashes and good fps. Hope this helps you.