The quickest way to get small screws out is to use a left hand drill bit, this is not a micky take - there is such a thing we use them all the time at work.
The idea is you run the drill in reverse (anticlockwise looking from the top) and as the drill starts to bite into the screw it will screw it out.
Make sure you drill in the centre of the screw, centre pop it first if you can and use a drill smaller than the core of the thread so you dont drill the carb body.
To find out the core size of the thread take the pitch off the major diameter - for example a M6 x 1mm pitch screw has a core size of 6 minus 1 = 5mm so you would use a 4.5mm left hand drill.
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