It's definitely possible to create some kind of rectangular map from them, but to be honest, I don't know what projection that would be. Currently the shader works by starting with a flat texture, and then applying a kind of 'spheriphication' filter on it. So if you just don't do that you would have a map
Yeah I think its possible to basically go the other way with how the math interprets the coords on the 2d object and project to a plane. ie It is possible to unwrap. I can post some godot code snippets or a paste bin or two if you'd like. (edit: atleast thats what I recall being able to do but its been a min since i've worked on the project.)
And sorry for the slow reply, I've been busy cooking on another project.