The more I dig into the Edge of Midnight fanfiction project, and the base map for it that I've been building over the last couple of months...and all the digging into HYGMap I've been doing as a consequence, the more convinced I've become that the sector-numbering system as explained by Geoffrey Mandel is just being ignored by scriptwriters in their day-to-day work. Easier to name the sectors after something particularly notable in each sector, and move on, it seems.
Though it seems like there was a system before Mandel's though, as the system seemed to begin in early TNG, and carried over into Star Trek, and then tailing off by the time of Deep Space Nine.
In fact, in the virtual forum video by Larry Nemecek about Stellar Cartography, we get a close up of one of the sector charts used (from 'The Naked Now' and from 'The Mind's Eye') and see that sectors are arranged in vertical 'belts' where they go up by 100 each column. So it runs from 20965 to 21065, 21165, 21265 and so forth. Albeit at a scale and resolution generally impossible to see.
And then we see a very similar system in use in the episodes 'The Wounded' and 'Redemption Part 2' on background tactical screens. Except there the numbers seem to go up by 1000, in horizontal 'belts' instead. so the USS Phoenix begins it's attack on Cardassian ships, around sectors 20497 to 21497, in that instance. With the same basic set up seemingly on the Tachyon Detection grid.
Obviously, the scale will not match too well, with ship movements, etc. But mostly it's been outdated, I think, by the grouping together of many different numbers relatively 'close' together, as in near Rura Penthe.
Still it does give a good insight into the minds of the set designers and behind the scenes thoughts.
