How small is a 12BA? Yet another option, if you have a mill, is to get some cheap carbide endmills from eBay or other sources, assuming you can find some small enough. Spin the endmill as fast as you can, and peck out the screw.
I had to do this recently after breaking a tap in a part - in my case, 2mm endmills were an appropriate size. Obviously, the larger the endmill, the less fragile!