on amazon (and elsewhere) there are small ez-out bits which are left hand bits and taps which may work. they come in a pack of 4-5 various sizes. (down to 2 mm). Its a two step method. First is to drill a very small hole in the head of the screw and then use the left hand ez-out to extract the offending screw. I would use a fair amount of downward pressure on the ez-out which is counter intuitive to get the screw to come out towards the force.... I have not used them for such a small screw but they work well for 1/4" screws and larger. You will have to be really careful not to go too deep with the drill but deep enough to have the ez-out to catch the edges of the hole. good luck.
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