Do we know for sure if the near instantaneous travel times we've seen so far are just a result of editing out the actual time of ship travel?
Basically, we don't. Indeed, the only time when editing
cannot plausibly be blamed for short travel time is unrelated to warp at all - it's the ridiculously short time in which as ship near the Moon falls down to Earth when her ability to hover is taken away from her. In terms of physics, that should be days, no matter what; in the movie, it's mere minutes...
Hey, in The Original Series, The Animated Series and the classic movies, the Enterprise went beyond the rim of the galaxy twice, visited the centre twice and made it back to Earth inbetween.
We could fudge that by pointing out that the definition of "rim" must be something else than the edge of the dish that is Milky Way, because "rim" stands between Earth and the Andromeda galaxy in "By Any Other Name" whereas the edge of the galactic dish definitely does not. The "rim" could basically be a fictional phenomenon very close to Earth, then.
We could further fudge it by observing that in "Magics of Megas-Tu", our heroes only want to observe the center of the galaxy - actually going all the way there is not mentioned, nor would it be a good way to observe. In ST5 in turn, the journey is supposed to be impossible chiefly because the Great Barrier stands in the way; this fictional phenomenon could again be close to Earth, and the adventure of our heroes would end right after their encounter with the Barrier.
However, the other thing about TOS is that it never mentions any part of the galaxy that would be
unexplored or
unreachable, except in terms of being forbidden somehow. Our heroes seem to be familiar with all parts of the galaxy already, even if their organization hasn't actually visited all the points of interest, and there are still some details to be sorted out on individual planets even fairly close to Earth.
I'm sure there is some old episode where Kirk or Spock have said "X% of our galaxy is still unexplored" or words to that effect, but I can't think of anything now.
Me neither. In the original continuity, the figure still was just 11% explored in early TNG first season, and 19% explored in middle TNG second season - an explosive increase as such, but indicative that Kirk had plenty of galaxy left to study back in his day.
I'd guess it's pretty much the same amount in the alternate universe as the original.
Agreed. Even if they did come up with superfast drive technology between the split in 2233 and the 2260s, and fitted it in all of their ships (including the older ones seen hopping to Vulcan in what could be interpreted as being a very short time), this might not yet make all that big a difference... After all, even if travel time was cut, the actual survey of each given star system would still take the same time, and there would only be so many ships to go around.
Timo Saloniemi