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Specifically in answer to Robs question: Gave this dilemma a lot of thought. Drilling-out for an extractor is not likely going to work as the extractor may expand the jet as it engages, making the matter worse. Trying to blindly center a drill (and a small one at that)will be extremely difficult. The hole on the jet is about .015" so it is of no help. Also: the brass is hard making it difficult to drill at best.
This might work for you if the slotted end of your idle-jet isn't too badly buggered. Per the picture, place an air-gun nozzle into the matching Idle-air screw hole (without the idle-air screw of course) and with Max. P.S.I. see if the jet can be blasted out. I tried it and it worked but I used an idle-jet that could be removed already, as there is no burring on it. Don't want to state the obvious but position the carb body with the jet facing down over your work bench and place a towel on the bench. If the jet is blasted out the towel will help in preventing the jet from ricocheting off the hard surface of your work-station and disappearing into oblivion at the speed of light
Let us all know if this works for you