What does an average,typical person know about the scale of the universe?
They might know that:
One) Every planet is part of a star system, just as Earth is part of the Solar System.
Two) Every star system is part of a galaxy, just as the Solar System is part of the Milky Way galaxy.
Three) Every galaxy is part of the Universe.
And possibly a lot of typical, average people don't know as much as that. But the English language has no commonly used words for other levels of scale in the cosmos, merely these three: Star system or solar system, galaxy, and universe.
And there is a degree of need for words for intermediate levels between star system and galaxy, and between galaxy and universe.
And possibly the technical Starfleet 23rd century English vocabulary does have phrases or single words intermediate between solar system and galaxy, and between galaxy and universe.
So possibly there are phrases in 23rd century Starfleet English such as galactic sub region or galactic sub volume, and they might be abbreviated into words like galsubreg or galaxsubvol or probably even shorter. And possibly when 23rd century English dialog is more or less translated into 20th and early 21st century English such phrases or words are wrongly translated as "solar system" or as "galaxy".
So it is possible that the barrier in "Where No Man Has Gone Before" surrounds a region within our Milky Way galaxy instead of the entire vast Milky Way galaxy.
In "The Alternative Factor" Commodore Barstow calls Kirk:
BARSTOW [on viewscreen]: You're aware of the effect an hour ago?
KIRK: Yes, sir.
BARSTOW [on viewscreen]: You may not be aware of its scope. It occurred in every quadrant of the galaxy and far beyond. Complete disruption of normal magnetic and gravimetric fields, timewarp distortion, possible radiation variations. And all of them centring on the general area which you are now patrolling. The question is, are these natural phenomena or are they mechanically created, and if they are, by whom? For what purpose? Your guess, Captain.
And if Barstow meant that the effect occurred in "every quadrant of this galactic region and far beyond" he would be getting information that could be from places much closer than they would have to be if he meant in "every quadrant of this galaxy and far beyond".
In "Errand of Mercy":
KOR: Sentimentality, mercy. The emotions of peace. Your weakness, Captain Kirk. The Klingon Empire shall win. Think of it, as we sit here, in space above us the destiny of the galaxy will be decided for the next ten thousand years. Can I offer you a drink? We can toast the victory of the Klingon fleet.
And:
KIRK: We have legitimate grievances against the Klingons. They've invaded our territory, killed our citizens. They're openly aggressive. They've boasted that they'll take over half the galaxy.
KOR: Why not? We're the stronger! You've tried to hem us in, cut off vital supplies, strangle our trade! You've been asking for war!
And our Milky Way galaxy has a galactic disc which is about 100,000 light years in diameter and about 1,000 or 2,000 light years thick, and contains about 100,000,000,000 to 100,000,000,000 stars. So how could the Federation, and the Klingon Empire, two puny realms ruling mere hundreds or thousands of stars each, and with fleets of no more than a few hundred or a few thousand space warships, realistically fight over control of the Milky Way galaxy?
It would be far more plausible for the Federation and the Klingon Empire to be fighting over control of a sub region of the galaxy that might have "only" a million stars or something.
In "The Galileo 7":
Captain's Log, stardate 2821.5. On route to Makus Three with a cargo of medical supplies. Our course leads us past Murasaki 312, a quasar-like formation, vague, undefined. A priceless opportunity for scientific investigation. On board is Galactic High Commissioner Ferris, overseeing the deliver of the medicines to Makus Three.
So either the United Federation of Planets, or some other space government, is very arrogant to give the title of "Galactic" High Commissioner to an official, or else "Galactic" is a bad translation of an adjective that actually means something like "sub sub sub galactic" and better fits the area ruled by that space government.
So maybe She Ka Ra is supposed to be in the center of the the local sub sub region of the galaxy, or something, and only about one or two thousand light years from Earth, instead of being in the center of the entire Milky Way galaxy 26,0000 light years from Earth..
And maybe in "The Magicks of Megas-Tu" the
Enterprise went to the center of the local sub sub sub galactic region instead of to the center of the Milky Way galaxy. And possibly in "The Nth Degree" the Cytherians did bring the Enterprise D to the actual center of the Milky Way Galaxy 26,000 light years from Earth.
The disc of the Milky Way galaxy is about 100,000 light years in diameter and about 1,000 or 2,000 light years thick. An do course thee is a non physical, abstract, mathematical central plane in the center of the galactic disc halfway between the "upper" and "lower" edges of the galactic disc. And possibly the "great Barrier" is somewhere in that central plane. If so the voyage to the Great Barrier might have been only tens of light years instead of twenty six thousand light years.
What do we know about starship speed in the era of TNG?.
In TNG "The Price":
DATA: The data from the Barzan's probe of the wormhole are quite impressive, Captain. The wormhole delivered the probe beyond the Denkiri Arm, in the Gamma Quadrant.
PICARD: It would take nearly a century at warp nine to cover that distance.
DATA: The same distance could be achieved in a matter of seconds through the wormhole.
If the Gamma Quadrant extends for about 26,000 to 75,000 light years from Earth, traveling that distance in 50 to 100 years would require an average speed of about 260 to 1,500 c (the speed of light).
In "Where No One Has Gone Before":
PICARD: That's not possible. Data, what distance have we travelled?
DATA: Two million seven hundred thousand light years.
PICARD: I can't accept that.
DATA: You must, sir. Our comparisons show it to be completely accurate.
LAFORGE: And I calculate that at maximum warp, sir it would take over three hundred years to get home.
So travelling 2,700,000 light years for about 300 to 350 years would require an average speed of about 7,714 to
9,000 c.
In DS9 "Battle Lines":
SISKO: The other side of the galaxy, to be precise. The Gamma quadrant is seventy thousand light years from Bajor. It would take our fastest starship over sixty seven years to get here.
If seventy thousand light years is 65,000 to 75,000, and over sixty seven years is 67 to 68 years, average speeds of about 955.8 to 1,119.4 c would be required.
"In VOY "Caretaker":
KIM: Captain, if these sensors are working, we're over seventy thousand light years from where we were. We're on the other side of the galaxy.
Over seventy thousand light years should be about 70,000 to 80,000.
JANEWAY: We're alone in an uncharted part of the galaxy. We have already made some friends here, and some enemies. We have no idea of the dangers we're going to face, but one thing is clear. Both crews are going to have to work together if we're to survive. That's why Commander Chakotay and I have agreed that this should be one crew. A Starfleet crew. And as the only Starfleet vessel assigned to the Delta Quadrant, we'll continue to follow our directive to seek out new worlds and explore space. But our primary goal is clear. Even at maximum speeds, it would take seventy five years to reach the Federation, but I'm not willing to settle for that. There's another entity like the Caretaker out there somewhere who has the ability to get us there a lot faster. We'll be looking for her, and we'll be looking for wormholes, spatial rifts, or new technologies to help us. Somewhere along this journey, we'll find a way back. Mister Paris, set a course for home.
So travelling 70,000 to 80,000 light years in 75 years would require an average speed of 933.33 to 1,066.66 c.
At such speeds it would take years or decades to reach the central point of the Milky Way Galaxy.
In VOY "Flashback":
JANEWAY: It was a very different time, Mister Kim. Captain Sulu, Captain Kirk, Dr. McCoy. They all belonged to a different breed of Starfleet officer. Imagine the era they lived in. The Alpha Quadrant still largely unexplored. Humanity on verge of war with Klingons. Romulans hiding behind every nebula. Even the technology we take for granted was still in its early stages. No plasma weapons, no multiphasic shields. Their ships were half as fast.
So it should have taken TOS era starships twice along to reach the galactic center as TNG era starships, if the innate speeds of he ships are the only factors.
Many speculate that in different regions of space there are special conditions which can multiply the speed of warp factors by various amounts.
But perhaps the conditions that multiply warp factors are the same everywhere, and they vary over time? In that case "the Magicks of Megas-Tu" and
Star Trek V:The Final Frontier might happen at very rare times when the varying conditions produced hyper fast speeds at normal warp factors, and such conditions might not reoccur in the era of TNG.
And another possiblility is that there is a system of gateways or stargates, portals leading between different star systems. A starship could enter a portal, emerge in a second star system tens or hundreds of light years away, cross that stars system to another portal, and emerge in a third star system tens or hundreds of light years from the second star system,and so on.
And possibly in the era of TOS one or more very long range portals were known, so that the center of the galaxy could be reached in a short time in "the Magicks of Megas-Tu" and
Star Trek V:The Final Frontier . but that one or more very long range portals might have been destroyed, or closed off from use by Federation ships, by the era of TNG and no longer be available.