Well after more fiddling, I'm convinced it is the way that Apple Mail renders the IMAP labels and folders. As a test I loaded MS Outlook 2011 (version 14.3.9) on my Mac. It rendered the IMAP folders exactly how they are on the Gmail website, and exactly how they are on my iPhone (which is what I was expecting). This is the exact same Mac I use Apple Mail with and the exact same IMAP settings on Gmail's website.
However, I'm sticking with Apple Mail due to its integration with the O/S and iCloud, etc. In the interim I'll just move stuff to my "starred" folder via my phone. Not a dealbreaker but pretty annoying.
To review and to put it as simply as possible: My IMAP folders on Apple Mail are not displaying or functioning the same way that they did before Mavericks, or the way they appear on gmail.com or my iPhone (iOS7).
Good luck to all with the solutions presented. I'm going to provide Apple direct feedback via the mail application tonight and keep my fingers crossed for a fix sooner than later.