Capitol Hill applicant for JD/MBA

Hi everyone! I've done some searching and can't find much information on how well b-school applicants from Capitol Hill do. I graduated college last year and recently got accepted to one of Penn, Harvard, Chicago, or Stanford Law School. For the last year, I've worked as a Deputy Press Secretary for a U.S. Senator, and I'm deferring law school til September 2019 to work for another year with the Senator. I'm thinking about applying to do a joint JD/MBA at one of the above schools, but I'm not sure what my chances would be (given that it's not the "traditional" path of 4-5 years in IB/consulting).

For context, I had a 3.9+ GPA at a top private undergrad. I just started studying for the GMAT and got a 680 on a Kaplan Diagnostic, then a 610 (?) on my first Princeton Review Practice Test, but I plan to keep plugging away and hopefully hit 700 at least. Would being in at the law school help me get into the joint program? Additionally, would a couple of years as a press aide to a Senator be sufficient on the work experience side for one of these top programs? Thanks so much for any guidance you all can provide!