Hey, I worked for J-PAL this past summer and from what I found, they are really looking for people who have extensive experience with Stata and doing data manipulation and who have field work experience. If you've done any field research in India, I would really emphasize that on your application. It's true that most of the RAs are from the U.S. but I was told that they don't get a ton of international applicants.
I think your profile looks strong. Emphasize that you have research experience and try to become very comfortable with Stata because they ask questions about it during the interview.
Two alternative to J-PAL are IPA (Innovations for Poverty Action) and IFMR-CMF (ifmr.ac.in/cmf). They work very closely with J-PAL and I actually ended up working on an IPA project. A lot of professors are cross-affiliated.
p.s. being flexible with location helps - ie if you are willing to go anywhere, make sure you tell them!