Good guess.
But all we know is that Farpoint was at the edge of explored space - and the star Pollux, in Earth's immediate neighborhood, was
beyond that edge in Kirk's days, as per "Who Mourns for Adonais?"! So obviously the edge can't be a simple spherical surface, and any reference to it must be viewed in light of this.
In TOS, we've witnessed Kirk at least 900 lightyears out from whatever he thinks of as his home. He also made all those trips to the Galactic Barrier at the edge of the galaxy, which probably is thousands of lightyears away from Earth even in Trek parlance - and in "Where No Man", there is a Federation lithium cracking plant within impulse range of the Barrier. In TNG, the farthest real-world fixes were to mere few hundred lightyears from Earth as well, to places like the Pleiades, or Mintaka, or Omicron Ceti, but again the hero ship obviously loitered significantly farther out than that (even going extragalactic once).
In which direction could a Federation explorer have wandered for 8,000 lightyears before planting the flag? Antispinward would mean running into the Klingons and Romulans, in terms of modern Trek cartography, but our intrepid explorers could probably sidestep those empires and press on. The farthest known location in that direction would be Canopus, some 200 ly away. Coreward lies the Great Barrier, an obstacle that can be reached in a matter of hours or at most days at warp seven, so probably the Feds in Kirk's days didn't go very far in that direction. Antares would be the farthest known location in that direction, again mere hundreds of lightyears away.
Rimward we hear of visits to Gamma Tauri, Omicron Ceti, and perhaps the "real" Rigel (even though other, more proximal Rigels exist), so apparently no adversary blocks the way there for at least the first thousand lightyears. The outer Galactic Barrier might lie in that direction, although it would be more convenient to assume that it encompasses the whole galaxy like a disk or a donut, and that our heroes didn't travel all the way to the rim of the galactic disk for their occasional adventures with the Barrier.
Spinward we hear that the UFP has knowledge of Deneb (presumably Alpha Cygni and not one of the other Denebs closer by), which lies several thousand lightyears away. But for the 8,000 ly figure, there'd have to be a Federation "island" farther spinward than Deneb, and perhaps another "island" farther rimward than Rigel, with the span quoted by Picard stretching between those two.
Timo Saloniemi