First if all Coltrane had dental problems abscessed teeth and he had to play like that to protect himself, something your old reed teacher should have known and in many ways he was playing a clarinet or even double reed embouchure. Many classical sac players played like that. Yeah he was not very refiend on the soprano saxophone and he probably was not going for that.had a reed teacher decades ago who was focused on tone production and improvisation as spontaneous invention. He decried Coltrane for being a "biter," someone who supported the reed with his jaw instead of a good soft tissue embouchure, and as a memorized pattern player instead of spontaneous creator. I think he had a couple valid points.
Pattern player -- Geez -- people will tell anything to compensate for their own insecurities. John practiced a lot --- but he also had soul and intention when he played out. But let's get to it technically. The pattern playing was from hsi sheets of sounds period, particularly Blue Train and Gian Steps. At that point he was also studying Slomisnky's book on scale patterns, applied to the fast and radical changes of these tunes. Yes he was problem solving at that time but if you listen t there is beauty in it. MxCoy said that John was moving verticall or chordaly and also horzontallyu scalar and melodic,
By the time he did Love Supreme he had moved away from that . Sun Ship - the band was just given sparse directions as per Tyner as little as 2 notes
When I’m transcribing sax guys, I avoid Coltrane because there’s all sorts of weird squeaks and overtone
If you played the sax, many of those things are either multphonic or altissimo and there is a fingering chart for them. Maybe read Rascher's Saxophones Top Tones or ask a capable player to transcribe for you. You can also omit them and treat them as performance blunders and some probably are and some are intentional. Listen to new classical music written for saxophone, many composers include so called advance techniques in their pieces and literally squawks high squeaks . growls . It's part of modern saxophone pedagogy and I am talking classical
All saxophone players practice the overtone series if they want to develop tone and breath control