I recently had to make a similar project in Unity for CardBoard and was interested in your approach.
Instead of using a shader to flip the image around I found and modified a script to flip the normals of the sphere so you can apply the material and it will work with the standard shader. It’s on my github. https://github.com/matt123miller/UsefulUnityClasses/blob/master/Assets/Classes/FlipNormals.cs
Also we experimented with using 2 spheres and giving each a different layer, with each cardboard eye only rendering stuff on a certain layer. It’s a pain to set up but it did accentuate to 3D if you can line it all up right. Can’t remember exactly how we accomplished it now,