Yep, that’s what Greg described he realized he was doing (if I recall correctly) and I can relate to it as well…I’m sure many can…
That is due to a fundamental, instinctual misconception of how the instrument works.
Bottom line is that we can’t fight the horn, we have to find the most efficient shape for each pitch for our own anatomy and mouthpiece/horn, etc.
The fix is to re-train ourselves by gaining a new understanding of how the instrument works and reconditioning our subsconscious/instincts of how to change pitch.
Other than suggesting you go back to Largo and work your way back up, which I recommend doing multiple times–I did and I think many do and each time I do I feel a benefit from it.
I would start by making sure my initial setup is right (tissue, visualizer) and think about keeping the lips front and center and flat. We don’t need to roll the bottom lip under, tilt our head back / bell down to ascend just like we don’t need to blow harder.
Maybe start with changing Shape (pitch) at lower pitches with steady / passive air first and gradually get higher. The course follows that path as well.
Eventually, you’ll probably find the pitch at which you start to introduce extra manipulation of the embouchure that’s unecessary and focus in on that pitch.
All we need to do is to bring in the corners slightly to change pitch. Less air is required the higher we ascend AND the harmonics are closer the higher we go, so it’s easier and easier to get to the next pitch…(except for the pressure)…but, if you get the Shape right (leave the top lip relaxed) and push the tension into the corners outside of the mouthpiece (or the edges) and outside of the vibrating surface of the lip(s), then we maximize the ability for the top lip to vibrate as fast as it possibly can (faster vibration = higher pitch) and we can kind of use the pressure (I think…that’s the sensation I get…) to help us compress the air, which speeds it up / speeds up the vibration of our lips…I think… That’s my understanding at the moment, FWIW. I’m not an instructor or pro player, I’ve just spent a lot of time on this figuring it out / experimenting, especially the past 2+ years.
Bryan Davis (Airflow Music) who has some videos on YouTube describes playing high as using Falsetto–it’s not physically harder than playing lower, it’s just different.
I have caught myself rolling my bottom lip under at times as well, reverting to old habits on occasion. One thing I’ve done in the past that has helped me is to use visualization–I look down at the leadpipe as I am ascending harmonically or chromatically and I think about the air going through the pipe and trying to keep the air going straight through the leadpipe, visualizing trying not to let the air column touch the inside sides of the leadpipe but travel straight down the middle.
Another visualization i have used is thinking of the Air Column as a 3 dimensional / physical drinking straw and reducing the aperture by using the aperture corners to reduce the size of the aperture, pushing the inside portion of the lips into the air column enough for it to interact with the air (“like the vocal chords”) by thinking Oooohhhhh.
I do also get a sensation when I get up towards to top of my range the sensation of pushing my bottom lip/chin lower as I keep tension in the aperture corners (top lip relaxed).
Leading with the air (starting the air slightly before engaging the aperture), but not kicking with the air to change pitch, is also a big help to me. I try to pay attention / observe the feeling of the balance between Air and Shape on each pitch / listen to the sound for resonance / the feeling of freedom/ efficiency.