I was also having these stuttering performance issues that seem to match your description pretty closely.
It only happened on one computer, the rest were fine, some things that were tried included:
Different computer, same GPU
Different computer, different GPU
XP, Vista, Windows 7
Different internet connections
Adjusting FFXI's config options [eg. mip mapping, hardware cursor, resolution, bump mapping, sound objects]


I understand a related fix was already posted in this thread but hopefully this will add some keywords or assist in some other way.

On my laptop running Windows 7 64bit [Core i3, ATI Mobility 5650]
Removed ICS(Internet Connection Sharing) from my network adapters.
Updated ATI Mobility drivers
Removed/Uninstalled VMWare
Removed/Uninstalled Oracle Virtualbox

It wasnt until I uninstalled VirtualBox that the problem went away.

I'm not going to say this is a fantastic idea based on anything intelligible but if you're having issues with the stuttering and it was anything close to mine and you want to try something silly, try this:
1. Install Oracle VirtualBox (its free)
2. Restart
3. Uninstall VirtualBox
4. Restart
5. Launch FFXI
6. Post results!

Best of luck!