Three phantom monitors after upgrading to Mavericks
I came up with a workaround when I was finalizing the question: mirror only the phantom displays. To do this, go to System Preferences-> Displays and click Arrange (click gather windows if you don't see an option to mirror displays). 

While holding the Option key, drag the windows that you wish to mirror on top of one another.  (In my case, I mirrored all of the phantom monitors on top of one another.) Release the option key and arrange the other monitors as you like.