I set up a test server at http://test.whatsthatbug.com so I can implement W3TC instead of the other stuff I was using.
I added all 6 of my css files to the CSS file management section of the minify page. If you go to the URL, you'll see how it looks as opposed to http://www.whatsthatbug.com.
It does not seem to matter what order I have the style sheets listed in. It also does not change if I choose 'combine only'.
I'm probably missing something silly. Can anyone enlighten me or point me in the right direction?