Is the engine lighting reliable enough to do this?
If so, one can set up a render target to expose repeatedly like you would a film.
Since the end product you need is a texture and a screencapture2d returns exaclty that, it would elminate some work.
My idea behind it is that - assuming engine lighting is good enogh to call this scientific - if you have the light move at the proper RA/declination for your date/time and lon/lat you can get a pretty accurate solar map.
You just need to refine the way the render target captures to allow it to fill up overtime/expose correctly.
You can probably remove eye adaptation and give the engine very low light levels to get the final texture - which should already be in 0 to 1 range (unless you configure it otherwise)
Id start with a fully black/opaque landscape, see if the light catches enough to create white spots on the texture without reflectivity.
Change/alter from there …