Sun-centric Cartesian coordinates in light-years
- X is distance from sun towards galactic center
- Y is distance along the rotational axis of galaxy
- Z is normal to X and Y
This is the logical development as space technology progresses. At first, we don't know the accurate distances to far-away locations. If we started with the center of galaxy as origin, Earth's coordinates would have an error bound of +- 2600 light-years. Unusable for navigation.
Sun-centric system expands as we travel further. Close stars have coordinates like 4-1-0, while further away systems are still reasonable 232-32-17.
The angular version of Galactic coordinate system is logical for observing from a single place, as we know the direction much more accurately than the distance. However as soon as you have multiple planetary systems, the rectangular/Cartesian variant is more practical. Distance between two places can be computed directly from the coordinate numbers. Binding the coordinate axes to location of a star system and the galactic center keeps the coordinates relatively accurate over millions of years even as the galaxy spins.
Eventually a second central world will find its place. It is inevitable if travel speed has any limit. Which world will find importance depends on abundance of resources, easy travel and local developments. They will start mapping the neighbourhood relative to their own system, maybe using a letter distinguishing the systems. Thus A232-32-17 will be B0-0-0, and the cycle repeats. Dealing with multiple coordinate systems has its cost, so this will only happen when enough travelers consider B to be central and A to be some distant relic.