I like the list, and not to confuse things, but for me it is difficult to find the "type" or "genre" of Jazz I enjoy.
When I was younger I lived in the Yale district of New Haven CT and there were several Jazz clubs that would get visiting musicians to play with locals on their way to and from Boston or NYC.
Most everything I had listened to was a kind of Avant garde, Free Jazz that seemed as though the musicians were jammin' but highly structured jamming. Passing the solos from one to another building on or breaking down previous rhythms or starting a new line of progression. I never knew what the label was for this kind of Jazz but I sure do miss the style and I have spent years (not continuously, but as the urge strikes me) to find that style and feeling of Jazz out there and I have touched on it, but never felt like I hit gold in finding it.
Most recently my searching has lead me to Ornette Coleman (vinyl-This is our music) but I have gone through Chrlie Parker, Miles Davis, Dave Brubeck, Stanley Clark, and many others trying them out, listening to a cross section of albums they were the main focus of or colaberated with others on and I have yet to tap into that fun, energetic, spontanious, mathematically complex music that I listened to back in the early '80's. I am sure it is out there, I am just not very good at locating it.