Thanks for the example project. This might be a C3 limitation. Once we change zHeight, it looks like C3 then does a pre-draw which breaks how the Alpha Discard effect works.
One possible way is to not change the camera to be parallel to layout, but keep it perpendicular. Then it may not be needed to change the zHeight, but instead can change bounding box size.
The big issue here is that then you probably can't use the normal behaviors to control objects because of the screen orientation.
Transparency & C3 remain a difficult issue for models like this.