AFAIK, the only thing that combines galactic quadrant graphics with labels for local detail is the Voyager
route map, glimpsed at Astrometrics in Season Seven. At that sort of resolution, we can't tell whether Earth is at the zero meridian, or whether some other part of the UFP nucleus is - the inaccuracy would be on the order of a few thousand lightyears. That the Alpha/Beta border splits the UFP in twain is more or less clear from that graphic, though.
It's difficult to think of a "non-political" way to define the zero meridian. On the other hand, it's probably a good idea to have that meridian rotate along with the galaxy, rather than be defined in terms of something external to the galaxy. Differences in rotation speed will "soon" redefine any borders based on the meridian, but the "soon" is a matter of millennia if the meridian rotates around the galactic center "attached" to one of the star systems belonging to the UFP. It's not a real, practical problem then. A meridian "attached" to a star system much farther from the core, or much closer to it, let alone to an outside point of reference, would create more immediate political problems...