RE: Adjustable triggers on Black Powder
Shootin' in the dark here, but if the rifle's trigger only has ONE adjustment screw it is probably only for weight of pull and would not fix your problem. Increasing weight of pull might help a little but ?? Generally such screws follow the lefty-loosey, righty-tighty rule.....loosen to reduce weight, tighten to increase. Overtravel and sear engagement would generally be separate adjustments and apparently are not included on your rifle.
So, my best advice is to leave it alone.