Most of it (original and TNG) actually takes place in the 'alpha quadrant' only. DS9 introduces the wormhole to the gamma quadrant, and Voyager is mostly about the trek back from the delta. Warp 9 is garbage in the grand scheme of things eh! ;)
It took the Kelvans 200 years to get from Andromeda to the Milky way. It would have taken Voyager over 30 years to go the 30,000 light years from the Delta Quadrant.
Andromeda is about 2.5 Mly away, or over 80x the distance that Voyager would have had to travel. By this we can determine that the Kelvan ship was about 10x faster than Voyager.
Voyager was 70,000 light-years from home and it was said on the show they needed 70 years at warp 9 to get home so the velocity of warp 9 must be 1,000 light-years per year (365 earth days) plus the whole faster than light thing which disregards the usual light year in a year thing. That's 2.74 light years per day which seems low considering Warp 1 is supposedly equivalent to the speed of light.
We've been lied to all these years it's all fake man!
"the velocity of warp 9 must be 1,000 light-years per year"
And by the way OP did not directly point out that warp 9 is 1000 times speed of light and my intention was to point that out to make sure they did not get confused by their own calculation which might have led to their underwhelming impression.
Seeing OP's response to one of the comments below (warp 9 factor = 834 ) validates my assumption that OP was lost in his own calculations for a moment. Only they can confirm.