I'm in college guys you can't just go play football or baseball. You have to be really, reallly good to even try out for those teams. Besides they don't even do varsity letters.
An important little tidbit of info that you left out of your original post.
So short of that, what I'm asking is how can I show my teamwork/leadership skills. I also asure you that while you get on the mat alone there are no individuals in a Judo club, it's a family.
Ok - let's start over from the viewpoint that you are a college student. You can't join the High School soccer team and earn a Varsity letter or be team captain.
So what to do.
Sports participation (athleticism) is important to the academies because they are physically tough.
A Varsity letter shows, among other things, proficiency in that sport.
Being Captain usually shows that you are respected as a leader by your coaches and/or teammates.
So how do you overcome not being on a sports team at your college, not being able to have a Varsity letter or being elected team captain?
In lieu of a school sports team:
Have you considered an intramural team sport?
If there is not one available that interests you, organize one that does. You like Flickerball or think that forming some Quidditch teams would be fun, and neither is at your college, then go for it (which would also show leadership skills).
How about running and competing in meets, locally or regionally.
Everyone can run. It is in your best interest anyway to begin running as a preparation for the CFA and the Service Academies ( you will run a lot at West Point).
In lieu of a Varsity letter:
Is there a way to show your proficiency in Judo? Do you have awards? You mention that you are an assistant instructor so you must be at a certain level of proficiency. Think of ways to show that on your application. Same goes with boxing.
In lieu of a being a captain on a sports team:
Here we are looking for leadership skills. What are some ways that you can show that off the sports field (or mat in your situation). Since Judo/Boxing are considered individual sports, you need to show skills in working with a team.
This is one of my favorite posts that gives an example of being a leader without being in an elected position. It's about what you do with what you have.
http://www.serviceacademyforums.com/showthread.php?t=11383
You mentioned being in a few organizations. Organize a group project. Take the lead and follow it through from beginning to end. Lots of opportunities there. A food drive would be an example. If you can't think of any ideas for a project, pick a charity (animal shelter, veterans home/hospital, Salvation Army, homeless shelters, etc) and contact them to see what your group can do for them and take the lead on that. You mentioned that you were involved in the Student Government (which is a leadership position), but this is a great group to organize a campus wide project. So many opportunities.
Organize something - lead the effort- and follow through with it.
There are opportunities out there to show leadership qualities and potential. You just have to take the initiative and do with what you have.
Judo and boxing are fine. Keep Judo up and consider taking up boxing again.
There are cadet/mids at the academies that did not participate in team sports, were not team captains or Varsity letter winners.
You have to think beyond those being just a check mark on your application, but the WHY behind those being a check box on the application.
Physical fitness that shows that you can handle the vigorous physical environment at the Service Academies and leadership skills.
My post is just some ideas of alternative ways to show that you are physically capable of surviving the SAs and that you have leadership potential.
Hope it helps.
Good luck!
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