Peoples and cats - I think it would be good at this point to consider some of the teachings of Donald S. Reinhardt. He talks about the forward pressure coming from the chops needing to equalize the back pressure coming from the trumpet which increases as we ascend. DSR used to talk about the 'Maynard Ferguson Doughnut' - You can clearly see in pics of The Boss the ring of muscle around his chops and how the forward pressure is balancing out the back pressure. In Lynn Nicholson's newly released and excellent instruction video, he addresses these ideas as well.
Let's take the ideas of two great brass teachers, Earl D. Irons and Carmine Caruso and combine them for a way to maximize our efficiency of pressure usage and to train the playing mechanism to function optimally in regards to pressure. I'm talking about Irons Group 20. At a comfortable volume, I would suggest trying to see how much of Group 20 you can play without removing the mouthpiece from the chops and breathing through the nose. If you are using too much back pressure from the trumpet, you probably won't be able to get far at all. Excessive back pressure will cut off the sound when attempting to do these big intervals on one, smooth embouchure setting. When you can do all of Group 20 without taking the mouthpiece from the chops, you will probably find that your chops are very balanced and efficient, and you will be playing the trumpet with great ease - from a physical standpoint.
As far as the trumpet, I think Patrick makes a good point. To determine if it is more the trumpet or your playing mechanism itself, I would see if you can play the 'E' at all and it just has a squirrelly slot, or if the 'E' simply doesn't speak. If it is the horn, then I believe you should be able to get the 'E' out but it may 'pop' up or down to the next partial..and you find yourself doing a 'lip bend' to get the E to come into some kind of tune. I think about playing some flugelhorns where the Low C is flat.. the note comes out, but it is not in the right slot..so you have to lip it up.
I just thought of something else - if you can get someone else to play your horn that has a comfortable and easy range above high C, that could tell you a lot! Best, Lex