Greg,

As an engineer, who had to take and understand a lot of physics and math, I will restate what you said, as I understand it, to see if I am getting the gist of it.

Your lips are vibrating sympathetically to produce a specific pitch. More flow at the same aperture (same length of vibrating membrane) results in higher pitch. Expanding the aperture, with the same air pressure, results in a greater length of vibrating membrane, resulting in a lower pitch and greater volume.

Think of a string: take a string of a specific length and tension and pluck it, and you will produce a specific pitch. Pluck it harder, you get the same pitch, just louder. Lengthen the string, maintaining the same tension on the string, and you get a lower pitch and lower volume for the same plucking force. To get the same pitch with a longer string, you need to induce more tension into the string.

Does my analogy work?