I cut a groove just above the thumb hole of my tenor recorder, such that I can tilt (and never lift) my thumb off.

The thumbhole of my recorders acquire a groove as a result of constant use. The result is that I lose adequate control over the notes in the high register and so I have to have a bush fitted to rectify the problem.

What you have done WAV is to create this problem and sooner or later you are going to have to do something about that groove if you wish to improve your playing in the upper register.