Sorry I missed this thread earlier as these locks are right up my alley.
Do you have an original Parker Hale (made in England lock) or is it one of the later ones where they used italian parts in the lock?
How did he "lighten the trigger pull?" Did he cut down the full cock notch on the tumbler? If so, that's one of the worst ways to do it and causes you to have to do ALL kinds of work to the other parts. A MUCH better way to do it is to soft solder (with a NO lead soft solder) a brass shim on the curved portion of the full cock notch. The shim needed is usually about .015" but can be as much as .020" if the notch is real deep. Sometimes that causes the trigger pull to go light and then you just file the brass until you get enough trigger pull weight.
The first thing I'm wondering is if the nose of the sear has already been damaged by hitting the halfcock. I've seen the sear nose broke of dinged up so bad from even one time hitting the halfcock that you have to replace the sear. I've also seen the halfcock broke from this happening at least one time, so I'd suggest you check them first.
Something I figured out years ago on all "musket" or large military locks is to take the springs off and put just the tumbler, bridle and sear on the lock with the screws holding them in place. I carefully set the sear into the notch and then very softly push up on the sear tail until the sear JUST comes free of the full cock notch. Now, hold the sear there and very softly rotate the tumbler. The outside end of the half cock usually or often will hit the sear nose. I file the end of the half cock notch until it just clears the tip of the sear nose. What that does is give you a little added insurance that as long as the shooter holds the trigger with at least the same amount of pressure as it took for the sear to release from the full cock notch, it can’t hit the half cock notch as the tumbler rotates on around. I have also seen it necessary to deepen or adjust half cock notches so the sear nose “flows” into the notch easily.
I have worked these locks for people who came from all sorts of shooting backgrounds and those who “grew up” in shooting high school or college .22 rifle competition are the worst for not holding the trigger enough as the hammer falls.
You should also check to see if the tail of the sear is contacting the wood inside the stock and keeping the sear from being pulled far enough away from the tumbler so it doesn’t go into halfcock. That is a common problem on repro muskets.
You should also check to see if the top of the trigger plate is pushing the tail of the sear up far enough so the nose clears the tumbler. Not real common, but I’ve seen it.
You should also check to see if the tail of the sear goes below the lockplate as it rotates. I’ve had to heat and bend sears so the tails don’t do that.
Finally, please, Please, PLEASE do not set the hammer on half cock and then pound or slam on the hammer “to see if the half cock notch will fail.” I can’t tell you how common that stupid nonsense is amoung reenactors, skirmishers and yes, even some International Shooters. The Ordnance Manuals of the 1850’s and 60’s DELIBERATELY mentioned you should not do that as it will cause damage to the lock parts and those parts were better than the average repro lock parts we have today. At the World Shoot in Wedgnock, UK, I caught one foreign “arms inspector” who was deliberately doing that to screw up guns of competitors from other countries. I waited until I got him alone and told him I had better never catch him doing that again and I would watch him. I also warned competitors away from his table. The “normal, approved” way to check a half cock on a musket lock is to put the hammer on half cock, hold the musket and rotate it muzzle down and then hold the weight of the musket with your trigger finger and WITHOUT pulling the trigger. If the half cock holds the weight of the musket, then it is serviceable.
The original English made Parker Hale locks are a joy to work on compared to the Italian repro locks and if that is what is in the musketoon, it won’t be nearly so difficult to get a nice trigger pull on it.