In Feathers containers, setChildIndex() affects the order of the items in the layout, and not just the depth. Unfortunately, there is no way to change the depth only.
You could set the child's visible property to false, and then create a copy of the child to add to the PopUpManager. That's probably the best workaround.
Alternatively, replace the child with a different object that has the same width and height, and then add the original child to the PopUpManager.