Thanks for reaching out.
I do think HBS is probably out, just because the average GPA is so high there. I think you could take a run at the others, especially with your international focus and strong leadership traits/experiences.
Taking a few classes is helpful because as long as you get As, it will show increased maturity, discipline, and focus. That is what is implicated by your low GPA - not intellect. Your GMAT score (which, sure, could be a bit higher and if you can score better, you should retake - but its in the range it needs to be to get you a read) is what speaks to intellectual horsepower.
That low GPA is going to work against you on two levels:
1. As a raw number, it just makes things tough, because a school has to absorb it into their averages, which of course impacts rankings. The thing to do here is apply to a few more schools, give yourself some safety in numbers. Also, focus on bigger schools (it is easier for them to absorb your #s) and even schools that don't put as much of a premium on GPA. Ross, for instance, is pretty big and notoriously lower than most elite programs on avg GPA.
2. Thematically, it makes them wonder about your focus. So what you have to do - even more than take a class - is articulate that focus, maturity, and discipline in your applications. There are many ways to do it, and it will make the biggest difference of all.
Make no mistake, 2.45 is going to make this an uphill battle. But we've had clients do it. I had a friend get into Yale with a 2.2. I would recommend adding Ross, Columbia (they care more about career goals than grades), Cornell, and then a 6th school, and taking off Harvard.
Hope this helps!
Respectfully,
Paul Lanzillotti