Hi Adam -
Officially, you've gone as far as you can go. "Unoffically", we're just serving web pages which use CSS for look and feel. If you're handy building a web site and understand how to modify style sheets, they're not hard to find on the Tableau Server machine. However, finding / modifying them is completely unsupported and not really recommended.
Another (supported!) idea might be to use embedding to drop a viz directly into your company's site - that way you get the benefit of all the "branding work" you've already put in on YOUR site without having to try and recreate same inside Tableau. You'll find info on how to do this in the same admin guide you're working with now.
Thanks for the help!