Hi,
I actually think your profile is pretty decent and don't count yourself out for the top programs just yet. I've heard many "horror stories" about admissions for elite departments, but my years of experience have taught me otherwise. Yes, some people (risking sounding racist, typically Asian students) have near perfect, if not outright impossible grades and credentials, but I've also seen decent but not superman like profile at top departments too.
Admission committees are likely to look at the overall chance of success in a research career, rather than only quantitatively assess numbers and class ranking, undergrad school reputation etc. Of course, some schools are more into numbers than others. My personal impression is that University of Washington, Seattle, and Purdue seem to rely on numerical formula to make decision. Admission outcome from these schools seem outright predictable. But other schools are much less regular. I've come across a profile for Wharton PhD admit that I personally would not recommend admission to schools in top 50 departments. Somehow, the applicant is admitted, and successfully graduated and placed at top 50 school. So you really never know.
Virginia Tech is a great school with a strong engineering reputation. You can really try to leverage that by looking into departments that have a strong technology focus. Off the top of my head, I think Georgia Tech has a small strategy group that is almost obsessed with technology related issues, which I think reflect the school's overall orientation. University of Illinois, Urbana Champaign has an excellent program, which unfortunately is consistently undervalued due to poor MBA ranking. Their strategy group has a few "rising stars" faculty that most people in the field are familiar with, but have yet to reach superstar status yet (Prof. Rajshree Agarwal, Prof. Joe Mahoney). These would be the decent shot for you. I think you would have a good chance at these two departments.
I would recommend looking into top departments, (Wharton, Duke, Harvard, MIT, Toronto, etc) and see if your research interests match with the faculty research focus. Trust me, having a great match is much much more important than having pefect scores. This is the #1 misconception in admission profile. Yes, if you look at average numbers, of course top departments have the luxury to cherry pick and bump up the average number. But it does not mean that there is no variance in their admitted pool. And more importantly, even if you manage to place yourself at top department, a poor match in research interests would just suck the fun out of it (if there is any fun left at all in this highly demanding career). So I would not recommend top placement over "right" placement, in gnenral.
Last but not least, I would highly recommend contacting current students and try to get their honest assessment of the program. Try to find out about "inside" stories. Your future relationship with your faculty is a highly asmetric one. If you are so unlucky as to have an abusive, manipulative, selfish, and treating-student-as-paper-writing-slave kind of faculty advisor (I used to have one!~), no matter how good the department is, you would not have a chance in hell to do well. Current students could be reluctant to discuss such a sensitive topic, you might need to have some social skills to sort of get it out of them. A good tip is to see if the current students appear somewhat reluctant, or reserved, in providing such information. That is usually a sign of abused doc students
You might know this already, but in general, strategy research is divided into the econ camp and the sociology camp. (econ camp much bigger). Think about what is more comfortable to you. Some departments are rather "ideological" in terms of the orientation. Some are known to be highly tolerant and intentionally diverse (Michigan, for example). So you might want to think about whether you want to pursue a generalist type of strategy research career, or a specialist one. I can't say one approach is better than the other.
Also bear in mind that business research "fields" or "areas" are not divided with strong boundary. In some department, strategy is located in the same group as organizational theory. Expect to see a more sociology approach there. OT is a bigger community so being in this type of research group gives you the benefit of being able to place at a larger number of departments. Some departments (Chicago, Northwestern) take a strictly economics appraoch and I would only recommend that type of program to those who can handle hard, abstract math. (real analysis, etc, but you should be fine with your background). The name of the groop could be very misleading! So be sure to look into what the actual research content is before jumping into the conclusion that "this is a strategy group." (I would not include Northwestern as a typical strategy group, it's rather an economics type of department, but the department is titled strategy and organization. I have yet to see any of their researchers publish in journals typically considered to be "strategy.")
BTW, don't let those who say "you need good publication" scare you. Sure, some students at top departments come in with good publication record, but I'd bet those are former joint papers with professors at master's level programs. In Asia, a lot of the "MBA" is more like MA degree and require a thesis to graduate. So this is not that uncommon for them. Yes, it they manage to publish at top journals before they even start a PhD program, it has some value in securing admissions, but trust me, the majority of incoming students to top departments don't have that kind of record. So you are fine.
Admissions to top departments is sort of like lottory. You can assess your odds, but you can never control it. I think your odds is better than most average profile I came across. But I guess my main point is even if you have perfect GPA, perfect GMAT, and graduated from MIT with a 4.0, your chance at top department like Harvard, Wharton, might be only marginally better.
best of luck