If you are using Windows 7, and thus unable to move the title-bar off-screen, you can turn off “Prevent windows from being automatically arranged when moved to the edge of screen”, found in “Make the mouse easier to use” (I believe that is in the “Ease of Access center” of Control Panel).

I'm quite certain that's the option that was OK enough for me, when I still used windoze.
Now I use Linux, and I can make anything, and/or everything borderless if/when I want to. ^^

It would be a nice option for FFXI itself, but I fear it might be too much work heheh...