I have purchased a couple of these auction muzzleloaders over the last year. One simply needed the trigger shimmed down to function properly as the hammer (cock) wouldn't stay back in the cocked position. The other one had a lock mortise so poorly inlet that I may end up using it for parts. Your rifle looks like its worth keeping even though it needs a few repairs / upgrades.
Its interesting to me that one of the screws that holds tumbler in place doubles as a screw that holds the lock in place. Improper assembly may effect trigger pull / tumbler function. See picture - screw is missing in the circled red section and I am assuming it is one screws that holds the lock in place too, otherwise you might be missing a screw.
You might look closely in the lock inlet for the trigger guard pin, I have seen a few pins that were placed hidden behind the lock assembly and the pin didn't bother to go out the other side of the stock making trigger guard removal more difficult.
I use the basic vent liner from Track of the Wolf
https://www.trackofthewolf.com/Categ.../960/1/THL-S4S
It increased my shot to shot consistency with out a single misfire by 400% over the smallest recommended drill size for a flash hole.
Attachment 282734