(West Point (like all the other service academies) is free to everyone accepted. You don't get full ride scholarships through family connections. You get a stipend while you are a cadet, and out of that you are expected to pay for uniforms and books, etc. But tuition, room and board are free. There are no scholarships except for further degrees.)
Your child's extreme anxiety related to doctors should show you that the anxiety is not just related to this one school. (It really is not normal for an 8 year old to behave as your DS does in medical settings). Exposure to an incident where he saw his own parent 'take down a full grown man in order to protect him and run out side of our home dodging bullets to save 2 friends' could very easily have caused PTSD. So could prolonged and unaddressed fear about your safety thanks to hearing details about your job as a corrections officer. He should not have heard any details about your job in a prison. He is too young for exposure to that aspect of life. I have friends who are prison doctors and they were very careful about how much information their children were exposed to about their daily work.
You are very immersed in military culture even though your lives were in the civilian sphere until your DS was 6, and therefore you may not see just how different your assumptions and attitudes are from civilian attitudes. Some of military culture is not a healthy model for children.
In addition, thanks to your career, you are clearly trained to respond to emergencies with a physical response (paramedic/law enforcement) and to deal with situations that are potentially volatile (in prison for instance) by means of tactics like verbal judo and actually tackling violent criminals.
Your preferred response to the school (in your head) is to grab the teacher by the hair. Your response to your child saying he would like to go to military school is 'Hell no!' -- you go into mama bear mode at home as well as at work, in other words. When things frustrate you or upset you, you have a physical or man-the-barricades response. If DS opens up more in future, try to cast your training and maybe your temperament aside and practice listening between the lines, so to speak. Ask him what would be good about military school. Ask him how military school might be different from regular school. Speak with a curious tone of voice, not accusing or deadly serious.
I understand it was unavoidable, but multiple moves and four schools from age 4 or 5 is not great either. And you are all off to Japan next year... Yes, military children move a lot (I have an exSIL who was all over the world by the time she was 10 and has no place she considers 'home') but your child seems to have had a lot of changes, and this can lead to deep-seated insecurity. There is nothing you can do about that, but there is much that you can do to try to understand how all of that may have affected him. Does he crave the school environment because it offers stability, predictability, or routine? Is that why he might like to go to a military academy? Or to West Point? I don't think a behavioral therapist is all he needs, though I can see how retraining his response system and habits of mind might be helpful.
Your DS has the impression that you are a tough cookie: his reasoning for it was that he would be seen as weak for being afraid of the boy, and for allowing the boy to scare him: he told my mother " mom is tough she isn't scared of anything she beat up bad guys at the prison and she wasn't scared I can't be either" Your 'resting personality' and the way you respond to situations that arise are perhaps a reflection of your training to demonstrate 'tough' and 'in charge' posturing. But that approach won't work to get a child to open up. He is already afraid of seeming weak. You need to drop the tough gal act when you are dealing with him, and seek ways to assure him that showing vulnerability and acknowledging feelings of weakness and smallness and reaching out to others are healthy ways of dealing with life's challenges -- you don't always have to go into superhero mode; life is far too subtle for that response anyway. It's fine for certain types of work. Not for home.
I think he needs a huge amount of reassurance that he can talk about feelings, and in order to accomplish that you are going to have to show him an alternative to going ballistic with representatives of 'systems' that you blame for problems (try not to blame at all), or venting in his presence. He shouldn't be living in a mental world where he feels he has to protect himself with thoughts of a superwoman mom, or where he has to worry in silence about mom in prison with hundreds of bad guys.
You need to look at the video games he plays too, and try to ease him away from them. 8 is too young for anything more complex than Oregon Trail (an old quest-style game) and other children's material. If he is playing games with any sort of violence then that needs to stop at once. If you are homeschooling him then you are ideally placed to introduce him to books and maybe even movies where characters express a wide range of emotions and responses and communicate in a healthy way, not just shooting lasers at each other, etc.