On that state recognition point (so nothing to do with immigration), looking again at the Respect for Marriage Act, I think there is a gap in the text where it comes to state recognition of foreign marriages. I assume they just wrote the law badly, as ever. I can't find any articles that discuss this, but then the commentary doesn't really focus on foreign marriages. The general lack of intrigue about the rest of the world in American discourse has actually been one of the most jarring aspects of moving to the US for me.
Anyway, I think this means that if Obergefell falls - and I do think that is a big if, even if a case is very likely to reach the Supreme Court - Georgia could deny state benefits to same-sex couples married outside of the US, whereas it could not deny them to same-sex couples married in another US state. Now that would require Georgia state officials to think about foreign marriages, rather than just focussing on not issuing new same-sex marriage licenses, which doesn't seem super likely.
For what it's worth, if I was in your shoes I wouldn't do anything rash now, but just make sure you have basic protections in place like a will, and medical and financial powers of attorney.
Word of warning - I'm not a lawyer in the US, and this is not my area of law where I am qualified, so I could be talking complete nonsense.