Conn 10Ms are well known for needing a large chamber mouthpiece to play in tune (yes, yes paulwl I know that actually once you push it in the chamber volume will be the same, but let's just agree to temporarily call it a "large chamber MP" for now). If you pull the MP out, whether just pulling it out, or extending the neck (thus having to cut off the little formed ring at the end of the neck, thus mutilating the instrument), or extending the MP shank, you will disturb the length relationship of the end of the MP with respect to all the tone holes.
Every MP/horn combination has a total tube length (this means the sax tube plus the MP) at which it plays the best in tune with itself. If the sax/MP are well matched, that tube length (= position of MP on neck) will yield A=440 tuning. If they are not, then A will be some other value than 440. For best results you need to investigate this. Of course you can compensate by lipping notes, but you are taking flexibility away from yourself. Also, with some horns having the total tube length off spec can create individual weird tuning anomalies (as in the notorious sharp middle E and F of Conn 12M baritones), and it can make altissimo very difficult.
I have had good tuning results on a 10M with: a copy of an old Link with a large chamber; Dukoff D7; Meyer 8.
A lot of people try to claim "it's all in your head"; unfortunately, they are using an analogy of a fretless instrument like a violin. No one tells a guitar player than intonation is all in his head. Everyone knows the frets are there. The tone holes are the equivalent of our frets. They are fixed in position. It is true that our sound production mechanism allows pitch flexibility, but you should try to have the horn requiring the minimum of lipping to play it in tune, then you can use the saxophone's flexibility for artistic effects rather than just trying to get the darn thing in tune.
Flute players struggled with this for decades: The old Louis Lot flutes were designed for A = 435. When standard pitch was set at 440, most people just had the head joint shortened so they could play in tune with the oboe's A. Unfortunately, by trimming the head joint and pushing in, they screwed up the scale. Then the Haynes "French model" flutes copied chopped-down Louis Lot flutes, and then Powell copied the same scale, and generations of flute students, when they got their first pro flute, were told that it was just that way, the high notes always sharp and the low notes always flat. But it was because the tone hole spacing was wrong; they were playing a tube with A=435 tone hole spacing, at A=440. Strangely, the Haynes Commercial models (closed hole) used a German model for the scale, which was much closer to A=440. Many student flutes in the 40s-70s were copies of the Haynes Commercial, so we had the odd situation where the cheapo student flutes played better in tune than the Haynes and Powells you had to wait 6-12 months to get. Finally, people like Albert Cooper and the Japanese re-figured the scales and suddenly you didn't have to lip the upper register down all the time.
This is not something mystical or spiritual, it's basic acoustics. Save the mysticism for places where it applies, like "how come Trane always sounds like he's saying something profound?"
