Anarchy, tough situation. I would suggest you read Bigbottom’s post above a few times. Really great advice there especially regarding the stance you, your wife and son are taking.
I don’t know your son at all except for what you have posted here. But, there are more than enough examples you have posted that would indicate why a teacher might give him low marks for character and leadership that wouldn’t show up on a report card or in a disciplinary action but might be reflected in an NHS application. Especially if they don’t see the good things he is doing outside the classroom. You mentioned political differences with teachers, ridiculing classmates (possibly in front of teachers and the rest of the class) for missing a question or getting a less than perfect grade, going above a teacher’s head on an issue, an older brother who was a troublemaker and a family who has on multiple occasions questioned teacher and administrative decisions to the point of having policy changed to (seemingly) favor him.
I don’t believe a group of teachers got together and plotted to get back at your son by giving him low scores for NHS. Teachers are usually way too busy trying to help kids to worry about screwing a kid over. I am guessing a few teachers came to these decisions independently and it’s not the system screwing your son over on this.
But, I don’t know much. So, take it for what it’s worth. To bring it back to college admissions, sounds like the letters of recommendation are already in. Here’s hoping you picked the right teachers. Best of luck to you and your son with this situation and your college application process.