It’s possible that your “Shape” is not optimal and that is causing more air being necessary to produce certain pitches. As you increase your efficiency, it will probably be easier to produce pitches higher in your range with less and less air.

If I understand your post correctly, you’re saying that you are using a “burst of lung and throat air” to play notes above the staff. Are you able to achieve pitches above the staff with passively released air, not actively supported air?

That was the key for me–separating Shape and Air by experimenting with Shape using only Passive air for quite a while. Then, once I learned Shape, I went back and focused more on my Air. That’s not the way the course is laid out and I probably wasted a lot of time, but it worked for me.