You are absolutely going to get in to most of the T14, and I believe you should set your sights primarily on the T6. As a fellow service academy grad with a 3.59, I can tell you that schools will be very forgiving of your GPA. They understand that your GPA is not the same as at other schools. Here's what Yale's Dean of Admissions, Asha Rangappa, has to say about this:
"The Law School Admissions Council (LSAC) — which compiles the numerical data on each law school applicant — provides, in addition to a student’s cumulative GPA, the percentile rank of that student’s GPA as compared with other applicants to law school from that same institution within the last three years. In other words, a law school admissions officer can (or should) see the difference between, say, a 3.7 at West Point (which would place that student in the upper 90th percentile) and a 3.7 at a school that is prestigious but has a lot of grade inflation (I won’t name names but a 3.7 can be as low as the 60th percentile at some very elite schools)."
And from Harvard's former admissions officer Karen Buttenbaum:
"The best way to illustrate this is with my favorite extremes: Harvard College (where the GPA college mean is upward of 3.5) and any US military academy (where the GCM is about 3.0). Someone with a 3.5 from Harvard is below the 50th percentile, where a 3.5 from West Point might be the top 15-20% of their class."
Your GPA will be fine to get you into any school. Your LSAT is already good, but you should retake until you get a 175+. If you were to get a 175+, I think you'd be in the running for a Hamilton/Rubenstein, in at HYS, and you'd be a lock for full-tuition scholarships at some of the rest of the T14. Schools absolutely do not care about multiple LSAT scores. They are desperate to keep their medians high, so a 175+ would make you an extremely valuable candidate.
One other point to consider is that HYS are interested in recruiting conservatives as well as military candidates. In one blog post, Asha says the following:
"For example, it's important to us as an institution to have a variety of viewpoints represented in order to foster robust and challenging classroom discussion -- to this end, we're very interested in having ideological diversity in each class. ... Another group of people from whom we like to see applications is our servicemen and -women. I personally have a soft spot for service academies, but my attempts to recruit on their campuses were unsuccessful."
To these top schools, military candidates enhance the classroom experience and are good bets to be highly employable. If you are also a conservative, these schools believe that you have a decent chance of clerking for a judge that prefers conservative clerks, hence you will boost the school's clerkship rate. I know that Yale especially is concerned about getting more conservatives and more military candidates. Normally the school gets around three vets in each class, but they accepted ten vets into the '17 class. If you are conservative, don't go overboard in signaling it on your application, but know that you shouldn't be afraid that it will hurt you.
Lastly, here are some service academy/vet profiles from LSN that can show you different outcomes for vets:
http://lawschoolnumbers.com/ACcommando
3.85, 174, service academy, got Yale, Columbia, UVA, Georgetown
http://lawschoolnumbers.com/bahama
3.6, 171 service academy, got H, S, Chi, NYU, Penn, UVA, NW, Duke, Berkeley, Michigan
http://lawschoolnumbers.com/SchusterFlook
3.6, 171, service academy, NYU, Georgetown, Vanderbilt, Chicago, UPenn, UVA
http://lawschoolnumbers.com/WAGB20
3.56, 163, service academy, Berkeley
http://lawschoolnumbers.com/lbr3
3.58, 164, service academy, Georgetown
http://lawschoolnumbers.com/matthewsean85
3.43, 168, service academy, Northwestern, Berkeley, Vanderbilt, Cornell, Georgetown, UCLA,
http://lawschoolnumbers.com/alabamagene
3.17, 163, service academy, Alabama
http://lawschoolnumbers.com/Drew
3.9, 171, service academy, Northwestern, Chicago, Michigan
http://lawschoolnumbers.com/goreman
3.79, 167, service academy, Vanderbilt, Michigan, Georgetown, his profile shows Harvard as pending, but he went to Harvard
http://lawschoolnumbers.com/nuke
3.6, 168, service academy, UT Austin, UCLA
http://lawschoolnumbers.com/jdough03
3.26, 174, service academy, Northwestern, Georgetown, UCLA, UVA, Michigan
http://lawschoolnumbers.com/Seaborn'16
3.5, 175, non-service academy, Stanford, Columbia, UVA, NYU, Duke, UPenn, Chi
http://lawschoolnumbers.com/twobitrye
3.42, 170, non-service academy, Berkeley, Georgetown, UPenn, Cornell, NW, NYU, UVA, Mich
http://lawschoolnumbers.com/r-t87
3.99, 166, non-service academy, Chicago, Duke, Georgetown, Michigan, Cornell
http://lawschoolnumbers.com/usafgirl
3.56, 176, non-service academy, NYU, Stanford, Columbia, Harvard, Duke, Berkeley, Georgetown
http://lawschoolnumbers.com/thedave29
3.61, 169, non-service academy, UPenn, UVA, Cornell, Georgetown, Cornell
http://lawschoolnumbers.com/ArmytoLaw
3.65, 167, non-service academy, Georgetown, GW