Selmer Series III Middle Register VERY FLAT
I've been playing on a Selmer Series III for a few years now, with a setup of Selmer Concept mouthpiece, SAXXAS Ligature, and Vandoren 3.5 blue box reeds. Last year, it came to my attention as I was playing with drones that my middle register (G-C#) are all nearly 20 cents flat. I shrugged it off and pushed past it with trick fingerings like fork F# for the G and G#, putting down the spatula G# for my A and using the side Bb key for my B and C. I've found my Bb and C# can't be fixed with trick fingerings, as I have to half-vent keys to get them to play in tune. The rest of my instrument plays fairly in tune, with just my lower E, D# and D playing a little flat.
The reason I'm seeking for a solution NOW rather than earlier is I'm in a quartet that is playing some advanced rep that has me in my middle register (eg. Maslanka Recitation Book mvt 5 where I have to hold out Bb's and quarter-vent my side Bb key while holding bis).
My horn has been to a repairman near me, where I was told my saxophone is in "the best condition he's ever seen" and that it has no leaks and should "play perfectly". I'm looking for a permanent solution to my intonation problems, not a "just use a different fingering" solution if possible.
I have noticed my neck is a little loose, so maybe that could be the problem? If I put a piece of paper around my neck it's too tight to fit into the body of the saxophone, so if anyone has a solution that I could try for that, let me know!
If there are any questions for me, I will respond as soon as I can! Thank you.
*UPDATE* I tested my professor's old Series II alto and the middle register plays in tune (B is about 5 cents flat but still HUGE improvement from my current saxophone), but the higher register is extremely sharp (C# being nearly 30 cents sharp).