It's hard to be sure of the issues your lock has without having it in hand. Here is a bit of information that may help.
- The bridel should be made such there is very little end clearance on the tumbler. This is what should keep the tumber from moving in and out, not the cock.
- The tumber hole and hole in the bridle should be closely sized to the tumbler so it doesn not wobble around
- The tumbler hole and bridle hole should be concentric.
- The tumbler shafts should be turned and be concentric with each other
- The hole in the sear should be closely sized to the sear screw or vise versa, to prevent the sear from wobbling around.
- The tip of the sear and tumbler notches should be properly shaped to provide positive engagment.
If these conditions are met, your problem should go away.