And Denniss... yes, up to a certain point, a lot of the high tempo stuff is scales, modes, arepeggio's. But the greats go beyond it. And move the harmonic structure behind what they are doing their thing on so much, it's hard to figure out WHAT pins it down inside their head while they do the scales.

I agree with you that, at least for me, MY solo improv style is to simply come up with an alternate melody, hopefully as strong as the main melody, and decorate around that a bit. Particularly coming from the 'bone (not as agile as most horns, unless you are Carl Fontana!) this being forced into a slower style allows my little guy inside my head to sing, and all I do is play what he sings. And the singing voice is nowhere near as agile as a sax!

In fact, what little teaching I do about improv mostly revolves around trying to get the student to link their voice with their instrument. Most of us can scat a reasonable decent solo on our voices. No instrument to get in the way, no fingering, no nothing but our minds and our voice (the most connected instrument to your brain you'll ever have). So, if you can scat a decent solo, just learn to play what you can scat! Easy..!

So I get them to do simple exercises, sing a bar, play the same thing you just sang. Sing two bars, play what you sang. Sing eight bars, sing sixteen... Pretty soon the connection between what you hear in your head and what you play is made. Your instrument now BECOMES your voice! And that's when the magic starts to happen.

Don't worry about anyone else's approach, whether confrontational or not. Let it go. Be confident in your own system, let the results do the talking!