This is a problem you'll find on most commercially available locks today. There is one thing that you can do without turning a new screw, without a lathe. If you have a drill press, or even an electric hand drill that you can strap to your bench to act as a 'poor man's lathe', set the screw in the chuck with enough of the head and shank exposed that you can slip a fine SAFE EDGED file between the chuck and the screw head. Dress the thickness of the nead down a few thou and try it in the lock. Continue removing steel from the inside of the screw head until you're afraid to remove anymore,m or until the screw will bottom on the lock plate without squeezing the bridle against the sear. You are limited with how much you can remove, but I have saved a few locks in this manner. Otherwise, make a new screw. Again, you don't NEED a lathe; a drill press and files will suffice, but a lathe makes it easier and more precise.