Broken pins in blind holes I must admit are one problem that can reduce to putting the whole shooting match in the trash. Though I do succeed in removing the broken piece more often than not.
I would strip the lock then use the two things that have a good track record of working in this situation, heat and cold. Because of the movement caused by heat and cold sometimes the the screw stub can become loose and turned out if there is enough to get hold of. I use Electronic freezer spray and a small flame butane torch a number of times in succession then add a couple of drops of penetrating oil then heat gently, this helps the oil to creep down the threads. I then work on the side of the broken stub with an old jewelers screwdriver freshly ground to be sharp, tap with a light hammer so it cuts in then using gentle taps towards the left seeing if It is possible to turn the screw. Another approach is to try to cut a slot in the top of the broken screw to take a screwdriver. As to the thread you say M2 it could also be BA 9 is 1.9mm and 8 is 2.2mm.
