Hell, the 1701 traverse 990.7 LY in a little over two days (See TOS S3 That Which Survives.)"It's going to be hard to reach the center of the galaxy in any kind of reasonable timeframe."
"Actually it's going to be super easy, barely an inconvenience."
"Oh really?"
"Yeah, they just go there in a matter of minutes."
"Oh. Wow. Are these ships just that fast?"
"I guess so."
[Six Years Later, Voyager Pitch Meeting]
"It's going to take them seventy-five years to go home? Why?"
"So the show can happen."
"But you established in the fifth movie Kirk's Enterprise could reach the center of the galaxy in mere minutes. Shouldn't this state of the art ship in The Next Generation era be able to reach one end of the galaxy to another in no time?"
"Oh. Yeah. Whoops."
"Whoopsie!"
^^^
Even if you discount the 30 minutes at Warp 14 and add a day (IE 3 days per 1000 LY) - even if speeds haven't increased in 100 years, the U.S.S. Voyager should have made it back in 210 days - and definitely within a year even if you add a stops along the way.
