All Seeing Eye
Admiral
...Although it should be remembered that the "We don't know how long Kirk had been working his way towards the Edge" argument doesn't work for the other two cases in TOS where the energy barrier was reached. In "By Any Other Name", the ship was in the middle of regular adventures, only weeks or months away from the previous adventure which had taken place within "civilized space", not all that far away from Earth. And while the ship's propulsion system there admittedly got a boost from aliens in order to reach the barrier, the ship repeated the feat in "Is There In Truth No Beauty?" without alien modifications.
Apparently, Kirk was able to reach the barrier at the edge of the galaxy as part of his regular adventures, without dedicating years upon years to the trip. We must look for explanations that involve fast ships or short distances, not ones involving long travel times, if we want to make TOS compatible with the rest in this respect.
Timo Saloniemi
But the question is how far does Federation space spread towards the edge of the Galaxy. You talk about "civilised space" so they could be located in Federation space (which is the civilised space to which you were referring) towards the barrier if Fed territory spreads very close to it.
As I mentioned before, there are safe warp cruising speeds, Voyager was cruising back to Earth at warp 6.4 (or 6 point something) so that would seem to indicate a 70 year trip home via 75,000 lightyears at a warp speed of warp 6.4.
So should a vessel on the outskirts of federation space on the way to the Galactic edge decide to warp at FULL warp speed they could get there in little to no time at all.