It's an interesting idea, but there's an added complication (which I apologize for not making explicit in the original post) which makes this problematic. Each of these objects is a cell in a UICollectionView (with a custom Layout). I rather fear that without overriding pieces of touch processing, the collection view will not treat the rotated cell geometry properly.

Another way of thinking of this problem is as trying to create a non-rectangular collection-view cell which responds based on its shape, not its bounding box.