I've done parallax scrolling as well, but this is obviously a bit of a different matter.
Doing the art for this sort of thing would require a lot of extra detail and redrawing of background objects. Honestly, it seems like a lot of extra work for something that probably won't look all that spectacular. I could see it done well for specific scenes, where something in the middle of the ring ought to be focused on, like if Juni were approaching some kind of monolithic space ship or something.