Here's my rationale for Sol being in Sector 001...
Current astronomical estimates place Sol at 25000 ly from the Core (almost exactly half way between Core and Rim), and 20 ly up from the Galactic Ecliptic. The Alpha/Beta border is explicitly drawn as a vertical plane through Sol.
Sector 000 has at its centre the intersection of the Galactic Ecliptic, the Alpha/Beta border, and the halfway point between Core and Rim.
Sectors are generally a cube 20 ly on a side. This conveniently places Sol at the centre of a sector immediately "above," or to Zenith, of Sector 000. That sector is designated 001, or Sol Sector.