Perseverance pays off again. This script works perfectly. The "exit" command at the end of the rsync command is what logs out of the Terminal when it's done. Thanks to Macscripter and the Apple Developer Website...so here it is:
The only thing you would have to change is take out the "-n" which makes it do a dry run so you know what will happen before you jump in with both feet, and change your username. And since it's checking "window 1" for the logout string you should make sure you bring terminal back to the front if you use something else so the script can find it.