This is the source code of script that Zenaku mentioned
You need to edit the value on WinMove line to match your screen resolution
You'll need autohotkey program to run this script
http://www.autohotkey.com/download/
Here's the step
install autohotkey
The easy way is open your notepad
copy the script I quoted and edit value to match your screen res.
save as yourfilename.ahk
run the script by double click
when FFXIV window start ( after SE logo ) you can press ctrl+shift+a to move it to psudo-full screen and no problem with alt-tab or lost lower border anymore.
Anyway.... I'm kind of disappoint that this script released since beta... almost 7 months ago.
And SE still don't take action on this issue
Btw, even with this script, if your window 7 go to login screen you still get some directx error and exit the game.
I know there's lot of issue to take care of.
But every minor things that SE neglect is like they are lag of good senior programmer to guide junior...