Harvard Business has the HBX program. If you do well in that, it may demonstrate some quant ability to offset your GRE quant score. The program is pricey though. You could also simply retake the GRE.
This little bit of advice is related only to HKS as I'm not familiar with other schools. Obviously, I don't see your essays, but one question I had is: Why education policy? If that was the hook for your application, it may have been a problem. I'm not sure if the non-profit you started was education related or if the law firm you worked for did education law, but I would make sure that, if you haven't already, make sure that your application makes a tight argument for why you will excel in education policy. Your recommendations, volunteer work, work experience should all make the argument. Remember at HKS they are forming a class of diverse perspectives, so there's only so many kids regardless of numbers who they will accept with education policy interests. A lot of those students are former teachers, school board members, legislative aides with an education portfolio, etc. So you have to make sure that your app really makes you stand out for your stated interest.
You're a great candidate, so I wouldn't get too discouraged about future prospects.