The reference you posted appears at first glance to be a site requiring considerable examination. Multiple artists have made statements. By posting that site it seems to me (and of course I could be wrong) that you'd like to see the concepts found in Stevens-Costello to be corroborated elsewhere. Okay fine but check this out.
Perhaps 50% of Stevens-Costello rests in one very simple concept. One which I'll get to in a minute. A totally gut easy one to understand and yet one which you'll almost never see posted or spoken of anywhere else. Herein lies a serious problem. Let's say that the concept (from Stevens) that I'm about to state is as easy to understand as a statement like this,
"Most fires need oxygen in order to start and sustain combustion".
Who would disagree? (okay technically you can also burn something with pure fluorine gas too but this is so rare as to almost be irrelevant). But here is the statement which I think comprises about 50% of Stevens-Costello. I'll start with a common quote from Roy Stevens. Something he was well known for saying.
"You can't play on your teeth".
There it is! Granted that the statement of Roy Stevens requires additional explanation. However from my background it is dead accurate and on the money.
The number 1 factor hammered in over & over in the Stevens Costello book is that the upper lip must be exposed to air. Occasionally Stevens uses the word "lip" in plural. His point however mainly refers to the way that the upper teeth can get in the way of the production of sound.
We can't see our teeth when we play. Both pairs form what is called the "Two Aperture Theory". To my mind it's less of a "theory" and more of a concrete fact. The lips form one aperture and the teeth the other. If the teeth close too much OR the upper lip doesn't set slightly below the upper teeth? The sound MUST always cut-off as one ascends into the upper register.
This explains why so many trumpet players can't play above a concert pitch high C. I once chatted online with a distinguished pro. Someone well known for his upper register. Not a major star but a lot of us would know of him. He absolutely insisted that his upper lip did not descend down past his upper teeth. He even further continued that his upper lip stayed even with the rim of the mouthpiece.
I responded that what he said may be so but I'll bet that just as soon as he sets his embouchure and places even a mild amount of mouthpiece contact pressure on his lips that at this point at least some small portion of his upper lip was remaining free to accept the force of air through it. Indeed there could be considerable variance in the amount of upper lip needed to receive the air flow. Perhaps the described fellow had a very elastic texture in his upper lip. As such only a small portion of it needed exposure to air.
But you can take Roy's statement to the bank. No trumpet player can produce a tone without first exposing his upper lip to air. Much of the Stevens system is locked up in this simple observation. It's not rocket science and doesn't require a blue ribbon panel to issue a peer review.
In fact before I switched totally over to the Stevens embouchure I still found it very helpful. Crucial in fact. In order to blow in connected registers up to high G.
Good luck all.