AA Male seeking OWL application advice Forum

[chun-li]

About me:
-AA male
-3.5 GPA from Swarthmore
-Two masters degrees from Harvard (5 year dual degree program)(No grades, but mix of HP/P marks)
-Took a course at Harvard Law while in grad school that I really enjoyed (and the professor has already written me a letter of recommendation for a fellowship in the past - not sure if she'd write me one for law school admissions but worth asking).
-Six summers of internship experience (largely public service) and very strong softs, but have only been at my first full-time job for a year (went straight to grad school from undergrad).
-GRE when I applied to grad school in 2013 was 157 (V)/159 (Q)/5 (AW). This converts to a 162 LSAT. (I think I can improve this with studying).
-Definitely aiming for T-14 schools (Harvard, Columbia, NYU, Penn would be my top choices).
-I conceptually enjoy what I pursued in graduate school, but looking ahead, I want to do something that is more policy- and people-focused and eventually go into politics.

General questions:
1. Does GPA and LSAT/GRE scores matter less if you are applying with an advanced degree and work experience? I have seen this posted in various threads, but I'm not certain how true this is. Is my GPA/GRE high enough for T-14 schools as an AA male with advanced degrees?
2. It seems like most admitted OWLs have 5+ years of full-time work experience under their belt. I would only have 1 year of full-time work experience when applying. Is this enough (even with advanced degrees)? I think I can make a strong case for applying even with just that amount, but do admissions offices prefer more for OWL applicants? My concern here is that I may come off as unsure about how I am navigating my career if I apply with only 1 year of full-time work experience. Would I be a stronger candidate if I waited to apply next year or the year after?
3. How much do diversity statements matter? I am a first-gen low-income student who grew up in a single mother household, and this is a big part of why I am considering switching into a career in law - to better serve disadvantaged communities.
4. I enjoy hanging out with people younger than me so entering law school at 28 or older isn't a huge concern to me.

Thank you for any feedback here!