The Pedersoli Kentucky pistols trigger pin is too far forward of the sear arm on the lock and there is not much that can be done to correct this.
That said, remove the trigger from the gun and use a fine grit black wet/dry sandpaper backed up with a small piece of wood to polish the top of the triggers blade. A 600 grit or finer should be used.
Polishing the underside of the locks sear arm that is sticking out away from the locks inner face can also improve things a bit.
The biggest offender is usually the sear spring.
This is the U shaped spring at the rear of the lock that is pressing down on the top of the sear.
To remove this spring after the lock is removed from the gun, loosen the one screw that holds it to the lock. Pry the rear of the spring away from the lockplate to disengage the tab that is in the slot on the plate. Once done, the spring will rotate upward, releasing its pressure on the sear. When this occurs remove the screw and the spring.
Hold the spring in a pair of Vice Grips (or equal) grasping only the lower part of the leaf.
Using a fine toothed flat file and filing only in a direction parallel with the leaf, taper the spring from the bend of the U (where no material will be removed) down to the tip. Leave at least 1/16 of an inch of material at this end to push on the sear.
Reassemble by inserting the screw thru the spring and into the lock plate.
Before the screw is tight, push the U shaped end of the spring down and towards the lockplate until the tab re-enters the slot. Then tighten the screw.
While your here, check the tightness of the screw that goes thru the bridle and sear. This is often tightened much more than is needed and it can cause a hard trigger pull.
This sear screw should be snug but not tight.
The sear should move easily and the sear spring must be strong enough to assure that the sear will always enter the full cock notch on the tumbler fully.
As for adding a screw to block off the distance that the sears nose can enter the full cock notch, I wouldn't recommend it.
First, the tumbler is hardened and it must be annealed to tap a thread into it. It then must be rehardened. Unless this is done correctly all sorts of problems can occur.
As the new screw could prevent the sear from fully engaging the full cock notch, unless it is adjusted correctly it could create a safety problem.