using a stereoscopic spherical skybox image for vr

I have successfully used a spheremap image as a skybox in Unity by setting its type to Cube, its projection to Sphere, and adding it to a skybox material, which I use in the Scene Lighting window.

However, I am now trying to utilize a stereoscopic skybox, where a version of the skybox for the left eye is stacked vertically on top of another for the right eye, for VR. It doesn't seem like Unity has this as an option using my current approach. How would I use a stereoscopic image as a skybox?