I have since made my own sky system from scratch and subsequently remade the material with better nodes:
I replaced the old 3 Point Level function with smoothstep nodes, and put in additional parameters, but other than that it’s the same technique as the initial post.
In the new sky system that I made, I opted to use a plane following the moon directional light and apply the material on that plane. This is done as I’m not using sky sphere, rather letting Sky Atmosphere doing its thing.
