Idle jets that won't come out past the internal "tower-cap threads" can be removed by the following method. It has worked every time for myself - more about patience than technique. The jet will remain trapped as a result of burrs from an improperly fitting bladed screw-driver used in conjunction with "Cro-Magnon" like force having deformed the ends of the slot in the jet.
Once loosened keep wet with WD40 or similar. Carefully turn in 'till it stops and turn out til loose. REPEAT several times.
DO NOT TIGHTEN! Heat the tower with a
gentle torch-flame then apply air pressure to the idle circuit intake port on the intake neck of body. Caution here! If you do not have a finger over the tower the jet will go into orbit! I always have a towel on the workbench surface and try do this procedure with the tower facing down
(facing the towelled surface) The towel will prevent "ricocheting" !
This method has never failed but in a lot of cases has required repeated attempts. Alternately rotating the jet CCW & CW while applying air can also assist. Keep in mind that the jet is of a harder material than the throttle body. The turning in and out is about loosening any solid material (rust/scale) that may have formed between the threads. The WD40 helps loosen and flush this material away from the jet/tower threads. The repeated turning in and out is as much about wearing some clearance between the tower-threads and jet threads. The internal threads of the tower will be what wears down. This is not detrimental to the tower threads. If the jet is otherwise free it is a good indication that any minute deformities of the jet-slot are minimal and plenty of tower-thread will remain. We're talking about mere .000's" of interference which is keeping the jet trapped.
In the '79 carb rebuild article I made specific reference to requiring 3 separate slotted drivers needed for removing the jets and tower-cap screw. Pre-soaking with WD40 ( or penetrating oil of your choice) and with a correctly fitting driver and a light tap with a light hammer to set the driver end into the slots and to loosen the threads/break free rust/scale debris.? Some heat works well here too ! Hope this helps