If I'm reading your OP correctly, and you have a decent quality automatic centre punch, do the following:
Using the centre punch, mark a dot as close as you can to the perimeter of what remains of the screw.
Starting with a gentle punch parallel to the screw. Wind up the pressure and mark, mark and mark again in the same spot, until you have a generous indentation in the screw.
Next, angle the punch tangentially to the circumference of the screw, place it in the indentation and resume the punching in an anticlockwise direction.
I've managed to free a couple of bolts that someone (here's lookin' at you, Pippa) had sheared in the top of a seat post.
I think they were 4mm - it should, with care, be doable with 3mm.
If they are seized, the shock of the punch should be enough to free them.
Failing that, magnets.
G'luck.