I forgot to update this question.
I found a TinyMCE/CKEditor plugin that really did the trick. It's called (surprisingly) PDW File Browser for TinyMCE and CKEditor and can be found at http://sourceforge.net/projects/pdwfilebrowser/.
It has a good range of different features and is really easy to modify (it has to be because it's me doing the modifications).
Definitely worth checking out.