Listening to George Garzone, I wonder whether he has published any method books about his approach? Has someone from the forum studied with him and could share his or her first hand experience with him?
I've studied with him privately & at the New School for 4 years in the past, so I think I qualify.
He told me that the triadic chromatic approach is something he came up with just for the sake of teaching chromatic approach to the improvisation. It's not really what he plays. He is not an intellectual type of player/person and he would be the last person on earth to write a music theory treatise. He is a natural genius type. He did often refer to the late-period Coltrane recordings, such as Transitions, but I don't think he ever transcribed or analyzed them. If anything, his primary influence is Stan Getz which you can hear in his wonderful sound.
His exercise for the students consisted of slowly playing random arpeggios of triads separated by half steps (i.e. GDB-BbGbEb-EGC-DbAF-etc.), gradually adding more half steps between the triads (i.e. GDB-BbAAb-AEC#-DEbEF-F#BD#etc.) until there are so many chromatic notes in between that the triads disappear. You are then free to play all intervals as you wish. Triads are only crutches. Having listened and played so much tonal music, he does utilizes tonal scales and triads, but he doesn't approach the music with any kind of systematic ways. It's all intuitive for him.
I would recommend that you listen to his recordings as well as other chromatic styles of improvisers like Wayne Shorter with Miles Quintet, Dave Liebman, Richie Beirach as well as 20th century composers like Schoenberg, Berg, Webern and Boulez, to name a few, and really saturate your ears to the chromaticism. Dave Liebman's chromatic approach book is really helpful as well. You will eventually find sounds and shapes that appeal to you and you can develop your style from there. Chromatic style is very personal and open.
Oh yeah, maybe you can study with him too, if you are ever in Boston/NYC area. He's really great to be with. God, I miss him so much!!