Humbly asking for your opinions on my MBA chances

I've only recently started considering for a rather drastic career transition (although honestly don't have much career to start with), and so far the forums on WSO has been greatly helpful. Please let me know what you guys think.

So here's where I stand.

-mid-20's male
-Graduated from feeder Ivy UG (political science, Summa Cum)
-Have been working 2 years in public sector (but has no "business-related" work experience)
-Initially wanted to go JD/MPP dual degree. Applied and recently been accepted to CCN law school and Harvard Kennedy School MPP.

Although I was admitted to a top law school, I'm not really excited about the prospect of becoming a lawyer. I'm trying to make a transition to consulting and I'm thinking a MPP/MBA joint (concurrent degree) is perfect for what I want to do in the future.

I have a fairly high oldGRE score (Q800, V780, AW4.5), and from what I know they are accepted in all the top MBA programs (ETS's GRE-GMAT conversion table says it's equivalent to 780 GMAT but I doubt it's that high). Should I still take GMAT?

To sum it up,

-Fairly high GPA but poli-sci major and no background in econ or business (reason being that I've only recently realized what I really wanted to do and that I need a econ/business degree to pursue it)
-Able to sell JD/MPP or MPP/MBA options to differentiate myself from classic applicant pool (which of the two do you think is better for raising my chances?)
-rather weak work experience (2 years in public sector). planning to gain some private sector experience over the summer and fall.
-High GRE score (but still take GMAT?)

So given my situation what are my chances into H/S/W, Sloan or Tuck? These are the only schools that HKS has concurrent degrees with, and HBS and Sloan is my dream/first choice due to their closeness to HKS.

Please give me your realistic advice on how I should go about doing this. If my chances are reasonable I am willing to throw away a decent option of attending a top law school, and I do want to make the shift to MBA.

Thanks!