You should be able to bottom the three screws of the bridle/sear, and still have the tumbler able to rotate freely. If the tumbler jams when the screws are hard down, you must remove metal from the INSIDE surface of the bridle to allow for some clearance. A few strokes with a lathe file will make a lot of difference.
If the sear screw forces the bridle down onto the sear preventing it to rotate freely, it is because the threaded section on that screw is cut too far up the screw. You can help by placing the screw into the jaws of a drill press, or even an electric hand drill held in a vise, and with a safe sided mill bastard file, remove some of the metal from the screw head's inside face - made the threaded journal a little longer. This will allow the screw to stop on the ends of the threads against the plate, while reducing the contact of the bridle against the sear.
Tuning locks to make them function better, takes an inquisitive and patient mind, to determine what the problem is, and how to remedy it.
There is no way you should be able to remove the fly without removing the bridle. If there is that much slop in your lock's guts, you have quite a few issues to overcome.