Revit :: Flip Object Vertically

I have an object, a non-symmetrical anchor clip, that has four configurations: Left Top, Right Top, Left Bottom, Right Bottom.  In the project, I can rotate the clip from the project's Top view, but when I try to rotate it from the Front, I get the message "Can't rotate element into this position."  In the family (see attached), I have a Flip Control in place to flip the element right-to-left, but I can't seem to add a top-to-bottom control in an elevation view.  To get the project out the door, I created a top and bottom version of the same object, but this seems redundant and makes my scheduling more difficult.
 
How I can either add another flip control to the family to easily flip the clip (preferably) or rotate the object in the project so that it is upside down?