I worked on a bari sax once that played a half step flat, even when an all-stater played on it. Thought maybe the mouthpiece wasn’t sealing right so re-corked it, didn’t work. I had a tech tell me to just double check and see if anything was inside it, took the gooseneck apart and sure enough there was remnants of a swab stuck inside. There was no extra resistance or any other playing issues, just played flat. Might be worth checking again, something could have fallen down the bell and get wedged into the bow.
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