I'd try taking a hacksaw blade & cut the end of the blade into a "V" shape. Use that to try & notch a slot into the stem, then use a tiny slotted screwdriver to remove. Like the ones that come in those precision screwdriver sets or eyeglass repair kits.
I'd try it, and stand a good chance of failing, but I'd try anyway.
Or, if you take out the welsh plugs, does one of them let you see the other end of the screw? Depends on the carb design, of course.