While there are physical matters directly related to solid range production these concepts seem (to me) to be less relevant than the ATTITUDE the aspiring lead player has. To preface:
I would bet good money that very few readers of this forum even have a solid High C to my satisfaction. Think this thought over for a minute.
Very very few trumpet players have a solid, usable High C...
OK now meditate on that for a few days and ask me for some suggestions. Wait here's one:
Develop a powerful register up to High C with lots of endurance, THEN expand to High F.