On farther reflection, I don't think the current plan is a good one. It works fairly well towards the center, but at the far reaches, the distortion will be massive. For example:
Take three stars, A, B, & C, all 100 ly from earth, with the following coordinates:
Star Bearing Elevation
A 90 0
B 90 89
C 270 89
As you can see, B&C are quite close together (3.5 ly), while A is far from both of them (140 ly ish). However, under the current algorithm, A&B will have the same coordinates, and be 0 ly apart, while C will be 200 ly from both of them. I have to wonder if this is a good idea.