Let's sort this out.
When I put a mouthpiece on my face and buzz, the lips flap open and closed and that produces a sound. For the time being, this is just noise. When I add the trumpet, the vibration that I set up by buzzing gets the instrument "resonating" and this also adds a certain amount of back pressure. As long as the resonance of the trumpet plus the strength of my chops can balance the air that I am blowing, everything is ok and I do not need more pressure than to keep the seal between my lips and the mouthpiece.
When our blow is more intensive than the chop strength and resonance of the instrument can support, our lips protrude into the cup and depending on the cup depth, can even "bottom out" stopping all vibration. Here is where additional pressure can "stretch" the lips somewhat, making them less prone to falling into the cup. This pressure cuts off the bloodflow to the lips and we now have the beginning of a desaster, the lips can't do their job, so more pressure is applied until the whole mess escalates to the point where we are wasted for the rest of the gig (or longer).
During this whole process, the trumpet and mouthpiece stay the same - this includes the resistance. The problem is that we have put our chops into a vice and they do not react predictably any more. Our air backs up and stress increases, causing body tension to increase, this causes our bodies to go into "panic" mode and the result is further escalation.
This is all interesting stuff, but does not help us on stage.
The solution is to increase chop strength through intelligent practice and proper care and feeding!
Don't practice until you drop, if you are in marching band, don't blow your brains out. Replace brute force with intelligence. Pace yourself. When you get a break, take it! Don't keep playing or trying to perfect a lick that should have been taken care of in the practice room. Less is more! Get used to using your ears and brains.
Supposed comments of 8 hours practice by Maurice André or Rafael Mendéz do not necessarily have ANYTHING to do with our reality. To PRACTICE in excess of 2 hours a day requires very mature chops and thinking process! One intelligent hour can replace 4 or 5 "random" ones. The goal is to replace muscle with brain.
Practice intelligently with your brain and ears turned on and you soon will not need to worry about "too much" pressure!