There is another alternative. Bill Brockway showed this to me and I've used it several times. The broken screw is 8-32, so you can use either an 8-32 or a 10-32 screw. Track's screws work well for this, as they're not super hard, but have some "body."
First, disassemble the lock and take the selected screw and mic the shank, not the threaded portion. Select the closest wire gaged drill bit to that size and drill out the offending broken screw. Lightly counter sink both sides of the lockplate.
With a very sharp cold chisel, cut several grooves around each counter sink. Cut a piece of the shank of the selected screw 5/16" to 3/8" long and heat it to red-orange. with your torch. While it's still hot, place it in the hole from the outside and peen it until it covers the counter sink. Flip it over and peen the other side the same way. File both sides smooth and the repair is invisible.