It would be nice if the sky matched the "actual" time tracked by Extended Days. I have some clues on how to do this. Forge provides a way to add a custom sky renderer to override the vanilla rendering method.

Some methods of note:
RenderGlobal#renderSky - Renders the sky.
WorldProvider#setSkyRenderer - Overrides sky rendering.

This still isn't a perfect solution. Other mods could override the renderer as well. And the renderer won't be a simple copy-paste, there are many private fields and methods used.

Another solution would be to use ASM to modify WorldProvider#calculateCelestialAngle. This may or may not work correctly if another mod overrides the sky renderer, but this might actually be the cleanest solution.