Congratulations on making a 730 on your GMAT and all your professional success to date! At a cursory glance, your GMAT, work experience, multicultural and global perspective, and impressive extracurriculars should open the doors to most of your school list. Your GPA seems to be the only sticking point, but working through your undergrad years could explain it and the fellowships certainly don’t hurt! HBS would likely be the longest stretch, but it would depend on the solidity of your overall application package, which would require watertight essays in terms of your goals and connection with the particular program.
Given your long-term aspirations, would you be interested in a dual degree? Some of the programs on your list like Fuqua, Darden and Booth offer the MBA/MPP or MPA, which might help you better build your network for a career in public service.
Let us know if you'd like to brainstorm together. We’d be delighted to help!