A lot has changed since then. The teacher that changed my flute life was Peter Lloyd, although I did get an overwhelming amount of information from a single encounter with Keith Underwood. These two gentlemen showed me how to bring about the best possible tone, with a huge increase in dynamic range(especially pianissimo), and tone color. The answer was very simple, just get out of the way.
I constantly remind my students and myself to open the throat, teeth and mouth and let the air stream do the work. The embouchure merely encloses the air stream, and brings the final bit of focus to your efforts. This works with almost every shape and size of lips and it is much less stressful on the body, the tone, and the music.
Understandably, an unrestricted air stream cause some other difficulties. We have to learn to balance the air pressure to the amount of resistance at our lips. Without some focusing, the air stream is broad and airy in quality. It works for most registers and situations, but not all.
It is true that the angle varies according to the register, the dynamic and even the articulation in use. If one exams only register, you might find that the best solution is often contrary to what our instincts tell us to do. This is especially true of aperture. When beginning the flute, we often find ourselves and our students with an embouchure that is wide open or too closed. The former produces an airy, unfocused sound which requires a lot of more breath. The latter inhibits the production of the higher register and causes articulation problems in all registers.
Here's a chart that I offer my students to help understand how to acquire good, open sounds in different registers.