Hello,
Take those classes! It will help! While the GMAT is obviously great and your experience has many strengths, taking a class and doing well in it will show, as nothing else can, that you can excel in the classroom as well as at work and at standardized tests. These top programs want actual evidence that you’ll excel in the classroom. Moreover, taking the class (or classes) will show that you acknowledge the shortcoming and are committed to addressing it in order to prepare for the MBA. I.e., it will show maturity. While you may be a viable applicant without taking additional classes, issue will make your candidacy far more idiosyncratic.
Another thing to do to strengthen your candidacy is to prepare yourself to make a really strong case for
your goals. If you haven’t done so, learn about you target fields and companies, including informational interviews. Show understanding of what the work is like day to day, and how you would position or market yourself for an internship or job. Develop a meaningful vision for your goals – what impact you want to have and why, and why this particular career path attracts you.
By the way, you might also be interested in MIT and Cornell. Both are strong in finance (even though they're not known as "finance schools") and I've found they both are very appreciative of applicants with a military background. MIT is obviously as competitive as the other schools you mention; Cornell slightly less so but still have some special qualities that might make it a good fit. Just a "brainstorming" thought.
Good luck!