However, your resume is super impressive, and you're clearly gifted. I'm going to bet that there will be people who will want to support your ambitions and create an ad-hoc internship for you. So here's my advice:
Treat your internship search like a job search!
Cold-call and cold-email CEOs of NYC-based startups that use Rails or React. Medium-sized and small companies might have an easier time accommodating, but it can't hurt to try bigger companies too just for kicks.
E.g. try this line for cold-calling: "Hi, this is Lachlan. Are you $CEO_NAME at $STARTUP_NAME? Yes? Cool! I'm a 13-year-old middle school student, and I built a web app with Rails and React last year. I'm looking for an internship this summer. I was wondering if that's something you'd consider."
Regarding child labor laws: Businesses with employees tend to already have a lawyer they regularly talk to (for contracts and compliance). They should be able to run the labor law issues by their lawyer for you - maybe you'll have to wait until your 14th birthday, maybe it's possible to structure it as a "trainee" program that falls under different laws, maybe something else. So I'd just bring this issue to their attention and leave it up to them to figure it out.