Vulcan redshirt, I enjoyed that link, and it seems your projections for Borg and Dominion space match well with Timo's "Star Trek Star Charts" book.
I agree the conquering empires likely would stick to mostly spherical territories. But the Klingons could be "down" from Earth regardless of which quadrant they're in and more easily have a literal sphere of influence that has lengthy borders with the UFP and Romulans yet remains within striking distance of Cardassia.
Placing the prime meridian at Greenwich may be arbitrary, but it's also a very useful spot to select for exactly the reason you cite involving the International Date Line.
On the other hand, the scientific definition of Western Hemisphere really does refer to everything within 180 degrees west of the prime meridian, but politically it's far more useful to refer to it as North and South America.
Timo, by the way I very much enjoy your book and read through it often. I suspect scientists would want to establish a prime meridian for the galaxy, as it would be essential for mapping purposes, and Vulcan redshirt's link suggests somebody already did.
I don't know how meaningful the alpha/beta line would be for the political and colonial needs of the Federation and its neighbors since exploration would be driven by the contours, or more precisely the stars of interest and astronomical objects of interest, of the Orion Spur.
The "Alpha Quadrant" really serves more as a helpful political shorthand Star Trek's writers invented. I just always found it amusing because the Dominion War involved such a tiny part of the total quadrant. It's like saying "the Western world" when you mean the Benelux nations.
I guess I think the Federation and Klingons should have been calling themselves the "protectors of the Orion Arm," or that Gul Dukat should have said the Cardassians were to be the "masters of the Orion Arm."