I have been watching this thread with interest since it started, but I have not had the opportunity to contribute until now.
My first thoughts when reading the dictionary.com definitions of balance was to think about the opposite, and what happens when balance is removed. Which in turn got me to thinking about martial arts: in arts such as Aikido, Judo and Tai-Jitsu in order to make your opponent fall or move in the way that you want to you need to take control of their balance and move it to a point where they are off balance, but not so far that they fall. Then you can control them.
Taking this back to turning I have been thinking about shapes that are either balanced, but look unbalanced, or unbalanced but look balanced. The only one I really have formed in my head is a round bottomed piece, with the Ying and Yang symbols on the top surface. However instead of the top surface being flat, the Ying would be recessed and the Yang would be proud of the surface, this would cause a weight shift in the piece, and it would tip to one side. You could then possibly have the dot on the hollowed out side filled with something heavy to restore the balance (maybe a sphere made of marble or metal).
If you want to add in another element of balance you can change which of the Ying and Yang are recessed or proud. Ying being female is typically seen as concave, and Yang as male is thought of as proud or phallic rising from the surface. If you switch which is recessed and proud then you are playing with the balance between male and female.
Of course I have no idea how I would do this technically