once you get close enough from c, all the stars in the universe appear to be either right in front of you, or right behind you

That's not really right. There is a distortion where things appear more in front of you than they are at the time you see them, but that's only because they were at that angle, but by the time the light gets to you they're not where they appear.

Also there's nothing that would shift light to appear behind you other than your movement away from objects that you have passed.