Well, I'm not quite sure what you want but I'll just contribute this and it's personal. What works for one doesn't always work for another.
In my first generation of trumpet playing I just was average. Played better than a lot at North Texas, not as good as others. Then I concentrated on writing and then on conducting, taking a long hiatus from playing. When I did get back to playing, it was on woodwinds (ww), not trumpet. I eventually came back to brasses.
One psychological thing was a carry-over from ww playing and that is, instead of a bunch of gyrations getting upper octave on WWs, you just moved your thumb. Yeah, you made a little adjustment but compared to what I had previously done on trumpet, it was easy and simple.
So, when I returned to trumpet, I used the same psychological concept. Keep it (octave jumps) easy and just think of flipping a switch, not going through muscled gyrations. That concept of playing easily served me well.
Pedagogically, I went to Jeff Smiley's The Balanced Embouchure and Maggio's book and system. My range went from the former workable range of A above the staff and a possible High C, to a workable E above High C and a playable Double High C.
I don't know if I expressed this well, but the point is playing with the least possible strain.