I am not sure I agree with your statement natedog, "You better downplay your military service because the academic elite are basically anti-military and anti-American. "
On the contrary, being a former military officer and a West Point graduate, I have found that top five schools are delighted to have military officers in their classes because military officers bring real world leadership experiences that no one else in the class has. This is even more true with military officers that have recently served in combat. Top schools are looking for well rounded leaders and they know that military officers are exposed to real world leadership scenarios that hardly anyone in their peer group has experienced. Of course I am a little biased, but that has been my assessment and all of my classmates assessments that are at Standord, Harvard, and basically every top 10 school in the US.
Now of course you don't want to talk just about your military experience, again you have to show that you are well rounded.