Sounds like you’re dealing with the dreaded octave key break. I have an exercise for this in my “How To Play The Saxophone” book. It’s basically an exercise that hovers around this” octave break” which is C# to D in the 2nd octave.

Practise where the break actually happens wich is those 2 notes, back and forth, up a few, down a few. You’ll notice the hard part is at this break and you need to adjust your embouchure and make sure you’re hitting the proper fingerings in time as well, because if you’re late it won’t happen.

Yes that would certainly do it! Good thing you discovered the problem.

Sounds exciting but I have no contacts there to put that together.

Not sure, but I would check the pad on your octave key. This is the one on the neck, if it doesn’t sit on the hole properly it can create a leak big enough to give you the problem you are describing. To check it yourself initially, play a note with your left hand in the range you have the problem, then press it down with the other hand while playing the note and see if this helps. It may even be a leak elsewhere so I would get it checked. As for jumping reed sizes maybe go to a 2.5 first…3 is a big leap from 2. Somehow I’m not 100% convinced that is your problem though.

there’s a few posts on that in the reeds section and I wrote a review and video on the subject.
I don’t use them. They have their upside which is always ready to play,last longer etc but when it comes right down to it nothing gives you the quality of a good cane reed when it’s in good shape.