So you are using the actual images from the telescope right? You are not creating images from actual data?
By the way this is a very broad topic just want to understand how your approach is first.
Cause of multiple subjects, unreal skymaps and texture, azimuths and data projection on 2d from spherical coordinates. Projection of 3d 2d is never perfect even its compansated on that images there would be distortions on somewhere like in polar sections where on skymap uv gets streched. You can compansate uv over there to appear right.
However if you want %100 accurate then already its another job which can be done too however I wouldn’t take image projection approach over there.