First, back to one of my original questions: I just wanted to insert into this thread that Warped9 did a remarkable job with a thread he started in May, 2011
Second, I would say "the impossible has happened" was Kirk's way of saying that Earth / the Federation assumed the Valiant had been destroyed and that the odds of finding any remains in the vastness of the intergalactic void were virtually nill.
Third, I do not have a problem with a Warp 1-capable vessel making to the galaxy's edge in a relatively short period of time (months or years instead of decades). It all depends on how you formulate warp velocity relative to the speed of light. If you use Cochrane's Formula from "Star Trek Maps", which assumes environmental factors affect that velocity, just as trade winds and ocean currents can affect modern aircraft and ships, then it is entirely possible even a low-warp starship, given the right course, could make it there much more quickly than if a faster starship took a different route. ("Maps" also suggested "slingshot effect" dangers from doing this as well.)
Where I break with "Maps" is the cause of this particular interstellar trade wind. "Maps" ties "Cochrane's Variable" to mass and gravity. I would tie it to subspace's relationship to dark matter and dark energy (TNG's "In Theory"). I assumed that the Valiant followed a dangerous trail of dark matter and/or dark energy to beyond Delta Vega, enjoying the remarkable velocity. But then the dark energy manifest itself as a magnetic storm they were unprepared to deal with, and the wild ride became too much for them to handle.