Pilot jet unscrewed but stuck in carburetor?

I'm rejetting my 2006 Honda Crf250x and I'm having trouble getting the Pilot jet out. It turns freely with a flat head screwdriver and if I tip the carb upside down it will fall partly out, but I can't get it to come all the way out even if I pull on it with a pair of tweezers. I can't take the float bowl off at the moment because the previous owners has mangled the heads of the screws. Does anyone know what the jet could be catching on or have any suggestions? Thanks in advance

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