But what about Trained ST?
The concept of Trained ST for bows already exists in a limited form in the form of Strongbow. It's a perk, and you get +1 to your ST at DX+1 and +2 at DX+2.
Trained ST uses this progression (well, that and more) already to extend the bonuses for Wrestling, going up to ST+5, or ST+50% if you like to level things up.
What I'd do is simply eliminate Strongbow, and make your ability to draw a bow follow the fast progression of Trained ST.
|Stretton and his 200# bow|
So your ST 12 archer could pull a bow of up to ST 17. This is basically "sport-specific ST" and I personally think it's quite realistic.
The use of "Arm ST" to push bow draw weights up might want to be curtailed. Maybe not, though. It's somewhat expensive at 5/level, and does represent a real thing. It's also often capped at 1-3 levels, but it would let you take a ST 10 guy and let him draw a ST 18 bow if you get three levels of Arm ST and are at DX+10.
I'm not sure that's a real problem, though. Yeah, your bow, which can only do damage once ever second-to-sixth turn in any sort of game where Fast-Draw and Quick-Shoot are not options, is your primary attack mode. You've invested (say) 20 points in ST, 40 points in DX, another 40 points for DX+10 in Bow, and 15 points in Arm ST - so you've just spent 115 points for the privilege of drawing a ST 20 bow, which does 2d-1 raw damage. Nice, but not world-shattering.