How to implement mirroring without double vision, distortion or chromatic aberration?

Unless you're on some really old version the mirror textures returned by the SDK should be unmodified and ready to blit.

What engine are you using? With Unreal and Unity, is should automatically display a mirror of one of the eyes without any additional processing. If you have your own engine, then you should already have the render target that you submit to the SDK, before the distortion is applied.