I've played flute for 50 years and feel confident about my abilities.
Sax a long time but didn't have much instruction or serious practice compared to flute.
On flute i change the air stream angle and shape for different registers.
For low notes a wider aperture and higher angle (almost straight across), for high a narrower hole and lower downward angle.
On sax I move my bottom lip/jaw slightly in and out thereby changing the amount of available reed for vibration.
Out for low (more reed) and in for high (less reed).
On both instruments these actions are graded throughout the whole note range.
Does this seem viable?