I see your point, I can't hardly visualise this kind of behavour until I have my hand on it in fact.
I'm even not sure we need a visual anchor, I mean what if the shape react like if you drag a surface.



when the mouse pass over the center of a closed curve, you highlight it ... and when you click/drag you see the [cen]ter grip, like when moving a surface.

Not sure what happends when different shapes share the same center, that might be a problem I suppose.