Locking down the throat, as you know, doesn’t help us; pressure can be a minimally effective short-term crutch, but hurts us as much as it helps us.
Believe it or not, releasing the air with the energy it has from the body and atmosphere is enough to play above the staff. We don’t need to Blow air into the instrument to play above the staff. Really.
J.gardam’s right, at times merely thinking of the higher note can work; however, we obviously are doing something physically different that may be imperceptible.
What helped me a bit is to Start with the Air and allow the aperture corners to respond to that air to obtain the pitch.
Playing above the staff requires a higher pitch, which requires a smaller aperture with the same air relative to a lower note.
Stand in front of the mirror and play a low C; pull the mouthpiece/horn off your face. Notice the size/shape of that aperture. Now, try a middle C… then a G above the staff… Compare the difference in aperture size between those notes.
Now, form the aperture size for a low C while looking in the mirror (without the horn/mouthpiece), followed by the G above the staff. How much tension was required to form the smaller (G above the staff aperture)? Did it require you to close your throat? No. Did it take a lot of strength, tension? Probably not…
There is tension/engagement Surrounding the lips to form Shape, not within the lips themsevles–that would reduce the vibrating capacity of the lips and reduce the resonance of our sound.
Resonance is optimal Sound and Efficiency and is the optimal balance of Air and Shape.
Like I posted on the other thread earlier, Clarke I playing softer as I ascended and focusing on Passively released Air helped me separate Shape (which determines Pitch) and Air (needed for long notes and volume).
And not giving a F*** whether you missed a note or not while using proper form in ascending was key. Experimenting is useless and ineffective if we are unwilling to fail, if we manipulate and use bad form (tight throat, using air as a crutch) to obtain desired results.
We must strive to be Objective observers to see what changes in Process effect Results, or we will continue beating our heads against the wall expecting different results…been there, done that.
Hope that helps, FWIW–good luck and every success to you!