I have a bad habit of wanting to help, but I have little experience and knowledge.
Do you think you are trying to engage the intercostal muscles by tightening the neck?
I am a retired science teacher, so I try experimenting. You can do some this analysis without using the horn and just breathing out through the mah-ooh embouchure.
The intercostal muscles come in pairs. The external ones contract during INHALATION, expanding the chest helping to create a low pressure so that air is passively pushed into the lungs by the greater atmospheric pressure. The internal intercostal muscles really contract when coughing.
If my understanding is correct, then intercostal muscles are not going to help to get air out of the lungs unless you are coughing.
So then the question is what muscles are you wanting to engage to create more compression? I paused here and decided to do an internet search. I think that there is an excellent article here to help answer your questions:
This is an article written for the International Trumpet Guild. I suggest everyone interested to read it and discuss the relevant points pick up from this and other scholarly articles.
I also look forward to Professor Greg’s teaching.