The reason why we use a flat map is actually quite simple. 3D on paper is too hard. It does not add to game play, its "close enough" to be somewhat realistic, and you simply can't do 3D well on a 2D surface of paper.
The NBOS software that Maspy linked is very cool. And with the pervasiveness of laptop computers, might not be much of problem to integrate a 3D map into games. If it performs as advertised when released, one can zoom, scan, or rotate the 3D map any way one likes. It will also compute distances automatically.
Using Bhoin's numbers, that means that known space is 1662.6 lightyears Spinward to Trailing, and 1043.2 lightyears Rimward to Coreward. But the disk out where we are at (28,000 lt yrs from the galactic core) is 2,000 lt yrs thick! The disk in this region of space is thicker than the OTU known universe!
[Couple additional astronomy facts. 1) the Orion Arm, where Sol is located, is about half way down the arm, along the inner (Coreward) edge. The arm is reported to be about 3,500 lt yrs across. Rimward of this arm is the Perseus Arm, and Sagittarius Arm is Coreward. Apparently the arms go, from Coreward to Rim, Norma (or 3kpc), Scutum-Crux (or Centaurus), Sagittarius (Sagittarius-Carina), Orion (or Local), Perseus, and Cygnus (or Outer) in a barred spiral shape.]