I think it’s great that you’re focusing on these sensations a bit.

Assuming you’ve got a slight overbight, like most people, then in theory I think you’re right–that your jaw should probably stay more forward.

However, I would avoid trying to make that determination objectively in a vacuum. I think it’s much more important to learn what movements you need to make by objectively observing what happens to your efficiency and quality/resonance of sound when you make movements with your jaw, embouchure, etc.

For me, one of the things that helped me the most with this is focusing intently, patiently, on harmonic slurs–I slowed them down, pausing extemperaneously on notes rather than sticking to the written rhythym…I slowed them way down, pausing on each and every pitch until that pitch felt and sounded right, then I would try to move to the next with minimal movement on consistent passive air (very important to take air out of the equation of changing pitch on harmonic slurs, IMHO).

As long as your jaw moving back isn’t part of a manipulation that you’re reactively making, such as when trying to ascend, then it might not be a problem–in fact, your body may be doing the right thing for YOU.

I had a tendency to keep my jaw back and roll my lip under, bell downward as I ascended. My instructor when I was young would say “roll the bottom lip in”. Now, I know that’s not the way to play. There is a role for the bottom lip/jaw to play, but the key (in my opinion) is to keep everything straight in the mouthpiece and rather than tilting/pivoting up or down too much, keeping everything centered in the air stream and not being afraid to have your lips in front of your incisor teeth (between your teeth and mouthpiece)…I think part of my pivoting and tilting when I was younger was trying to avoid my lips from being scrunched between the mouthpiece and my incisor teeth, but in my opinion it’s important for that to happen–the lips (in my opinion) contract towards the mouthpiece as the aperture corners are engaged and the aperture reduces inwards.

As you get used to this, it feels much easier and natural and (in my opinion) is simpler/logical. There is, at times, a sensation of “gripping” the mouthpiece with your embouchure as the lips contract forward towards the mouthpiece / around the air column.

One key is to avoid the tendency to tighten the throat/engage the body as you ascend–for me, around a middle C or E on the staff is a point in which I need to get past without engaging the throat /tightening up as I ascend, then it’s just a matter of gradually allowing the aperture to shrink slightly/gradually as you ride the air upwards. When things are going well, the lips are responding to/reacting / interacting with the air and I’m simply not doing anything more to get in the way.