It's your classical, clarinet-like embouchure. A thin bottom lip against the reed results in that nasal sound, no matter what mouthpiece. Too much mouthpiece can have the same result. I've seen it a million times in students and fellow musicians. For that big, lush tenor sound, you need a ton of bottom lip flesh on that reed, well supported by the chin muscles pointing up, not down. And take in enough mouthpiece to cover the gap between the reed and the rails, nothing more is needed. But a fat lip will cover before and past that point. There's definitely a sweet spot for every note on the horn. Check out some videos of Bob Mintzer and others for the classic jazz embouchure.
I think the physics of the fat lip approach is a matter of distributing the force over a greater surface area. Concentrating the force in a small area (thin lip), results in nasal. Spreading the same amount of force over 3/4" or so provides the same overall pressure needed to control the reed, but since it's not all in one place, the nasal component goes away.
No pressure at all is just as bad. If you take in too much mouthpiece, and there's no control whatsoever, resulting in a duck call sound. You have to maintain full control (pressure), but not all in one spot.
Of course a high baffle means more brightness. But a lot of brightness comes from the shape of the mouth cavity. When I want to brighten my sound, my tongue is shaped as it would be if I were making a whooshing wind sound, making the volume inside smaller, speeding up the airstream and directing it downward. Really hard to describe, but experimenting should get you there.
It's gonna be hard to change something you've been doing since the 70's. But use your ears as well as closely watch the masters you want to sound like.
In SOTW tradition, I'm sure the next post will completely contradict me. But the embouchure I describe works for me and many, many others.