I had a similar aggravation with a small Siler mounted on a pistol. While it didn't catch and hold at half cock it would momentarily "catch" causing the cock to slow down enough for a very weak flint strike. I examined the internals and noticed the fly was dropped down so far that I could see virtually the whole part. But once the fly was removed - a single trigger pistol - the problem disappeared.
Being an old John Deere Area Service Manager, I love reading these type posts...Reminds me of how I used to catch hell in the old days, mechanics would always chase their tail before we found the real problem and it was usually much simpler than they thought...
The bridle should be tight. If it binds the tumbler the lock was made incorrectly. Sear screws sometimes are threaded to far and need to be left loose.
I can not diagnose what I can not hold.
I will say, if the fly is necessary for the lock to function with a single trigger you have another issue. The full cock notch should be at the same distance from the center of the tumbler, or a bit further out. If the full cock notch is closer than the half cock not the lock will always be a problem. It will beat up the sear and cause function problems. This will be worse with a powerful sear spring and or a sear spring with the tip too short.