My point, Tom, is that you are claiming perspective is working in two opposite ways at the same time, on the same objects.
As two objects, which are an unchanging distance apart, get further from the observer, they will appear to get closer together. This is due to perspective, and is why you say the stars appear to get closer to the horizon as they get further away. Yet, somehow, the stars do not appear to get any closer to each other (only closer to the horizon), also because of perspective. This is contradictory, and makes no sense. At the same time, perspective is also keeping the stars the same distance from each other, as well as in the same constellation shapes, despite the viewing angle increasing as they get further from the viewer. "Perspective" is incredible!