I'd make all weapon damage be based on Str. EG: The difference in damage between a 100-lb draw-weight bow and a 150-lb draw-weight bow depends on your ability to draw the bow, and that depends on Str, even if aiming is still an issue of Dex. Also, crossbows shouldn't have any stat-based damage boost, but should instead have a value intrinsic to the weapon itself.
Dex-based to-hit for ranged and finesse weapons is fine. This is only a slight shift, though it's debatable whether it breaks the "100% compatibility" guarantee. It still feels compatible to me.
The Martial Maneuvers section goes a long way to making various stats more useful, because you can do so many new things, and I think it will help a lot with the Str vs Dex argument. Part of the current problem is not that Str isn't useful, it's that it's not useful in doing interesting things — primarily due to a lack of skills. Dex is similarly (un-)useful, but the few things it has are at least more visible, and it has more skills that can be applied in different situations.