The 1920s was "a long time ago" and the Andromeda galaxy is "a galaxy far, far away." Maybe the original trilogy took place 100 years ago in the next galaxy over.
It's just a faster route to get through a hyperspace dead zone it's a retcon but at least a somewhat logical one if you ignore the sapient hyperspeed space whales.
Yeah, and I'm fine with that. I don't need a "plausible" explanation for everything. Same with Star Trek. In Voyager, Tom Paris goes faster than warp 10, which is infinitely fast. And he doesn't travel infinitely far. Or all that far at all. How is that possible? The writers said so. Why did he turn into a salamander afterward? Because that's what happens when you go faster than warp 10. Whatever, as long as I'm enjoying it.
Edit: also, as far as I know, the TV show with the most people with advanced degrees who have worked on it is Futurama and they never let science get in the way of a good joke.
The Enterprise D Technical Manual that Sternbach and Okuda released, which was supposed to be about as canon as it gets, says warp 10 is infinite speed. Go figure.
Maybe it's Warp 9.9 that is ever increasing. I don't really remember, but I distinctly remember reading two different tech manuals describing the "fastest possible speed of any federation vessel" as two entirely different multiples of C, and Warp 10 being defined as the fastest possible speed.
That really depends on what you count as a Galaxy. If any cluster of stars that is gravitationally bound together counts, then there is a tiny (10,000 stars) galaxy that is orbiting The Milky Way that's only about 10,000 light years away from us, which happens to be closer than the center of our own galaxy.