The leadership angle will be good. Other things that I think could help give you a boost are the ability to deal with stress--I mentioned knowing how to tell simulated stress (a la my FTOs at field training, or the evaluators at a training exercise) from real stress, and being able to look put things in perspective. I'd also mention any experience you've had with interpreting regulations, ROEs, service instructions, etc. Is it safe to assume you had experience in "Coalition warfighting?" if you had to work issues of releasing information to other allies, and you can share them, it might be good.
I mostly put my service information in my resume, rather than a PS--although I mentioned it a good deal in there, it was mostly a setting for the main thrust of my statement.
About awards, I'm not sure how liberal your service is with decorations (we Air Force types tend to look like third world dictators after 4 years), but if it is I would definitely list the big ones and skip some of the smaller ones. (I.e. Marksmanship probably won't help you with law school, but any Quarterly or yearly awards, or combats awards, should be mentioned.) For example, I listed my Air medals, but ignored the training ribbons, National Defense, etc.
If you'd like, PM me and I'll send you the military section of my resume, if you need ideas for ways to try to use your service experience.