Yes agreed: I am not saying there is not a problem somewhere but all I am saying is that PI or 2PI is likely not it. (PI is usually a surface shading error, but yeah who knows everything is possible).
So there must be a fundamental problem somewhere else. Maybe something like the skylight captures the height/volumetric-fog into the environment lighting representation that is then used to lit it self again on the main view via the diffuse spherical harmonics. The SkyAtmosphere contribution is separated from that: this contribution is from a *atmosphere light scattering only value * (so this way of doing things for an unshadowed participating medium should be more correct than the skylight feedback loop). And it is separated to avoid that specific feedback loop. So again investigation is required within the wide matrix of all the interactions.
Thanks for those images, and I added all that in the long list of todos…