Wandering off-topic, but what if the concept of finesse weapons was dispensed with entirely, and instead you could choose Str or Dex with any weapon? What additional tweak would be needed to keep Str builds viable?
Allowing Str with crossbows and such would remove the dominance of Dex when it comes to Ranged attacks, in the same way that you're removing the dominance of Str with 2-handed melee, so that mostly balances out on the "Damage-dealing" front.
The issue is that Dex is just so much better as an ability score. As a combat stat it also ties in to AC and Initiative - Both very important.
Out of combat it has three skills attached to it and allows non-heavy armour to be used, which can be useful in exploration and social pillars.
In terms of adjustment, I'd suggest making Initiative based on a different stat, and tracking encumbrance.
That will remove one of the combat benefits that Dex has over Str, and make Str more important in the overall game. See how things go with those changes before doing anything more sweeping perhaps.
Oh. And allow half-feats that gave a bonus to Str but not Dex or vice versa to give the bonus to either.