You can use an axes object instead of subplot, that's beside the point. What do you mean with editing the axes? You are even using explicit handles, so what is your problem?
As I understand it, those handles refer to the specific object created in this figure, so using h after that close is impossible. What you can do is figuring out the object tree (just use get(object,'Children') and test for the type to be axes and the tag to be empty).
