Playing with wrapping #AllSkyCamera footage onto a curved surface in Blender to recreate what it actually films, just a quick try, but this has potential.
Somewhat unrelatedly, have you thought about setting up 1-2 additional cameras for parallax to the clouds?
I was thinking of giving someone a view of sky with clouds with a very large (at least tens of meters) effective intereye distance, thus effectively scaling distances down.
Technorama in Winterthur has a "distance magnifier" on the roof, which is basically a large pair of binoculars with effective intereye distance of ~2m that point horizontally and can be rotated around the vertical axis. That causes surrounding buildings to appear much less flat, so the obvious idea is doing the same to the view of clouds. I would guess that having 3 such cameras would already allow for some nonterrible interpolation for viewing angles where the line joining the eyes doesn't align with the line joining any two cameras (I suspect that being able to provide roughly correct view for slight angular movements is important for creating a realistic-looking view for humans).
@robryk Interesting....what are you thinking, depth perception 3D video stuff?