Hi Gustav,
The Davis Twigg lock has a number of issues, some of which you discovered. Here is an image of the inside of the stock lock.

The mainsprings are too weak, the flint cock does not over hang the pan enough at rest, the head of the sear screw fits into a hole of equal diameter without a shoulder so it does not press on the bridle at all. That was a cheap way to eliminate having to thread the screw precisely so it does not pinch the sear. The tumbler post sticks out too far such that the shoulder of the flint cock barely overlaps the bolster on the lock plate. Here is my rework of it. I first made a new mainspring of a length that allowed me to take some off the shoulder of the flint cock so it over hangs he pan more but the stirrup does not drop below the lock plate. The mainspring is much stronger as well and has the right geometry at full cock. I replaced the bridle and sear screws with ones that have bigger heads and stronger slots as well as shoulders that fill the original counter bored holes in the bridle. The sear screw has a second shoulder at the end of the threads so it cannot pinch the sear. The inside of the lock plate had to be flattened and then polished. I annealed the tumbler and filed the square shoulder down a little so the flint cock sits closer to the plate. I also ground down the hump on the feather spring a little and reshaped it to reduce the excessive tension on the battery and allow it to snap over at just the right time.

I will case harden the tumbler, sear, bridle, flint cock, top jaw, and lock plate when I am ready to case harden the battery and after cutting teeth in the jaws and engraving. It should be a good lock in the end.
dave