Warp speed may also refer to different velocities in different parts of the galaxy, similar to the Chochrane's Factor used in the old Star Trek Maps. Warp 5 may be faster in Federation space than in the Delta Quadrant.
There's a number of instances in TOS of the Enterprise travelling 1,000 light years in a matter of days. They could be using a subspace freeway that is a narrow corridor. Once you get off it, you'e back on the galactic surface streets with their lower speeds.
The truth of the matter is that ships move at the speed of plot. Accept that and you can accept all the rest regardless of any apparent contradictions.