Is there a way to save the Z-order?

Allowing the user to change the Z-order is clearly documented (MoveAfter and MoveBefore).
How can we save the Z-order information of each specific object?
Is there a Z-order property?

The z-order is the order of the top-level objects in the Document. In other words, the first item is the backmost, and the last one in the list is the frontmost.