Enlisted Nuke to Consulting Path

Are you looking to break into top tier firms or just any firm in general? Lots of 'consulting' work for government side in the ever-revolving defense industrial complex revolving door. If you're not trying to be super exclusive you can probably get away with average undergrads/online programs. You can just put on civvies and go right back to your old job in many cases as a 'consultant'.  If you're talking about M7/MBB that's very different. 

In general though as a fellow vet / good post-service MBA I would advise you to shoot for the moon on undergrad brands because of the doors it opens and the people you're going to associate with (and the employers who target those schools).  There's now a decent vet network at these top undergrad schools too so you may get hooked up with yellow ribbon/scholarships etc. I would advise against doing online programs because if you really want to make a complete transition from military to civilian employment, you're better off actually going to those schools in person and making the transformation. This isn't like a military school where you're just checking boxes for your training jacket, it's about meeting people and having a good base from which to meet with employers and explore career opportunities. If you're shooting for top MBAs and top consulting gigs, you'll need strong summer internships where again, much harder to get if you're not at a target school. Staying reserves is fine and could be helpful for continued work experience. The certifications are meh- I don't really know FMVA and if you want to see some fun arguments google 'CFA vs MBA'.  PMP is helpful but usually more for technical folks in engineering/construction, having a general understanding of project management is always good though. 

You also mentioned getting a top MBA (Duke/Ross are pretty strong)- this is going to be much harder IMO if you go to a clown online program. You're going to be evaluated on the rigor and performance of your undergrad experience as part of your MBA and competing with ivy league grads (and other vets, some of whom will also have stellar backgrounds)- so would you rather try to compete with a degree from an ivy or an unknown online program?  

IMO if I were in your shoes my 'dream' path would be- start targeting ivy or MBB target schools, especially vet-friendly transition ones (I think Columbia has one). Matriculate full time, be laser focused on either impactful club activities or finishing coursework to make space in your schedule for additional work experience during school. Get competitive summer internships in either consulting or banking, apply to one of those 2+2 programs like HBS where you can get accepted out of undergrad but have 2 years to get work experience.  Alternatively you could look to go straight from undergrad to MBA but this could be tough.  You could just convert your summer offers to solid full time role, 2 years then MBA, then back to consulting.  

Also for a 5 year contract- a lot can change in 5 years. You may be able to take a sabbatical, or even request early release from the Navy. A fellow unit member of mine actually did it because he got his HBS offer but still had several months remaining by his start date, and I was stunned when they let him go. Sometimes the forces are just looking to shed bodies.

Applaud your long-term vision but remember no plan survives 1st contact with the enemy!