However, I always had the feeling that distances were intended to be further apart in TOS* than was retconned into TNG (e.g. the Klingon homeworld was likely supposed to be 1000s of light years away, not 100), so the slower speeds generally work OK for TNG.Yeah, the chi factor is great for making the "official" cubed Warp Factor more akin to what TOS depicted in terms of extremely high speeds. It's not so good when applied to TNG era speeds, since they seemed to stick far more rigidly to the velocity's given on that series' warp scale.
* = off the top of my head the only systems that seem to close to Earth to not have been explored already assuming a "large" TOS UFP were Pollux in "Who Mourns" and Sigma Draconis in "Spock's Brain" - but maybe we can apply the same philosophy that resulted in the Rigel system being a different "Rigel" than Beta Orionis in the sequel shows