Nice work on getting started early as it will give you time to address current weaknesses in your profile and make you as competitive as possible for your target programs.
Side note: Congrats on the work with NSOF, my company has filled a handful of merch orders for you all since our two co-founders are both former Navy EOD officers.
As you've noted the biggest obstacle you'll face is the fact that your undergrad degree is from an online, no-name (to use your words) program.
For better or worse, top 10ish MBA programs tend to care a lot about the caliber of the undergrad school rather than GPA alone despite the fact that Ivies and public Ivies are notorious for grade inflation.
The two enlisted guys in my HBS class both got undergrad degrees post-EAS -- one from Dartmouth and one from Georgia Tech, and the GT grad actually got a masters in engineering there as well.
Here's how I'd address the undergrad issue since you've got a full year until you'll really get into the thick of your application process:
1. Build an alternative transcript via courses from bigger-name schools on subjects that'll be helpful in business school -- finance, accounting, statistics, high-level math, etc. A few schools like BYU and UCLA and probably several others I'm forgetting offer reputable online courses that MBA programs will usually take into account when judging your readiness
2. Shoot for 730-750ish on the GMAT if at all possible, ideally with a fairly even split between your Q and V percentiles. As a mil applicant who's lacking a heavy quant background from your undergrad major, you'd be better off with a 720 via 90% V and 85% Q than you would with a 740 via 99% V and 75% Q.
The big questions that you didn't really address -- why do you want an MBA, and what do you plan to do afterwards? Depending on how unique and memorable you can be with your answers to those questions, you could greatly improve your odds of admission over what they "should" be based on your quantifiable stuff like GMAT and perceived rigor of your undergrad program.
Other stuff to do in the meantime -- research a handful of other schools that might be good fits in terms of location/curriculum/culture/career goals/etc., get in contact with veterans at all of your target schools, get on their adcom email lists so you're informed about their admissions traveling roadshows and webinars and whatnot, and
if at all possible visit some of your target schools if you're able to get back to the States on leave while classes are in session.
As for handicapping your odds for those 4 schools it's a little hard to say absent the career goals bit, but as I previously mentioned having an interesting personal story in terms of what you've done thus far and what you plan to do in the future can go a long way.
Whenever asked for an example of how to do that, I point people towards this clip (
https://www.youtube.com/watch?reload=9&v=RuurulTCbZs) which I've heard from a few people is basically a video version of one of the essays that Jake Harriman wrote for Stanford about why he wanted an MBA.
That sort of story will resonate much more than "I want to be a banker/consultant" career goals, or plans that aren't really fleshed out in detail.
On the surface I would say that UCLA and USC (and other schools in the Texas/Michigan/UNC-ish range) are realistic targets given a 700+ GMAT and strong essays/recommendations.
HBS is a stretch but that doesn't mean you can't still apply -- it just means that you don't want to pin your whole future on it.
Stanford? Who knows, their admissions process is
very hard to predict -- at first glance I would say the odds are very slim, but if you're able to pull together a credible story like Jake's and get your application in front of the right person on their adcom then you could catch a lucky break.