The Ubuntu desktop is Unity and that is a different download.
Ubuntu 12.04 desktop: Unity.
Mint 13 desktops: MATE and Cinnamon
Default Gnome desktop (e.g. Fedora 17): Gnome-Shell.
If you wish to use Unity I think it's a better idea to simply use Ubuntu 12.04 rather than trying to persuade Mint 13 to use Unity. Haven't gotten around to installing Gnome Shell in Mint 13 yet.
Thank you for this thread. That’s all I can say. You most definitely have made this forum into something special. You clearly know what you are doing, you’ve covered so many bases. Thanks!