I have experienced a strange effect that could be the subject here - the note seems to change back and forth as though you're doing false fingerings. I've had this a few times mainly on bari on A and B III and the same on tenor but very rarely. It definitely is the mouthpiece and reed combination along with pushing a lot of air. I do not have a recommendation on which way to go with your mouthpiece and reed except you may be pushing too hard of a reed with whatever mouthpiece you're using. In my case, on bari, it ended when I returned to using a vintage Level Air. There has to be another way because most players are not going there and they really shouldn't, but I'm mentioning it as a reference. The Level Air has a huge shank bore that is wide open, an almost vertical step and a long, flat, high baffle to the tip. It looks on the outside just like it is on the inside. This might be saying anyone having this problem might need to try some mouthpieces. I know its impossible to simply notch down in reed strength after playing a harder set-up. Maybe a little more baffle is needed.
I had it continuously with a Martin CIII bari and Berg Larsen HR 130/1. I had the bari stripped and washed out because I suspected a build-up in the loop but it made no difference. After I got a new low A, I thought I was done with it but it still happened once in awhile until I went back to the Brilhart LA.