Or when you drop them, have the dropped tower snap back to the store, and read the mouse location like it was a click on the wall.
You can make a draggable window for your HUD, put all the parts in 1 or two families and pin the families to the draggable background image of the window. (the background can be in the family too.)
Set an event
Not touching dragbar | drop Windowbackground.
That way it can't be dragged if they aren't using the dragbar. (which could be the title font.) Which would keep it from interfering when you drag items out of the window.