Can you please make it so we can use a UIbutton, UIContainerBackground or an UIImage as the piece to control UIMoveHandle?

See this picture: http://www.almuramc.com/images/almura-2-3.png

We would like to be able to click a [ ] button next to the X to move the window around instead of the icon in the upper left corner of the window.

You would need to make that component yourself.