Unity: Rotate a 3D ball using 2D Physics

Unity is an awesome game engine with great 2D and 3D features. While working on a 2D game world with 3D game art, I ran into an unexpected challenge with rolling 3D spheres. Let's frame the problem in the context of a 2D soccer game with a top-down view.

TL;DR
Before (animated gif)
After (animated gif)
GitHub Project