<p>I'll give you a few thoughts, but understand that I got my MBA a very long time ago, so I'm not current on today's trends.</p>
<ol>
<li> Product design is not a normal MBA track. If you have a talent in that area, go for it!</li>
<li> Pursue what you love to do. In the long-run you will do better if you love your work, or at least find it interesting.</li>
<li> You do not need an undergraduate business degree to get into an MBA program. Many take econ or other majors.</li>
<li> In fact, for some MBA programs, you don't need an undergraduate degree.
I used to work with someone who was a Vietnam-era green beret, and he got into Harvard Business School after military service without an undergraduate degree. This is probably unlikely today because things are so much more competitive.<br></li>
<li> UVa is well-regarded. If you go there, don't worry.</li>
<li> It's not for everyone, but you can also look into Columbia University School of General Studies. This is an undergraduate school within Columbia University for older students. I know you take courses with Columbia College. I don't know if courses in the School or Engineering are open to GS students. They offer a joint BA/MBA degree, but you have to apply to the MBA program a year early, and there is no guarantee that you will be admitted.</li>
<li> I just don't know about military experience counting as job experience. If you got promotions and various awards, it might. Some businesses like the dicipline that a military background gives you.</li>
</ol>