I've been off the boards for a long while (and am only back now because I'm avoiding teaching prep!), so I missed this question when you first posted. I don't know if a move is still on the table, but I can totally identify with the unknowns of a national job search. In fact, this is the entire reason that we decided to get married-- I was going to be on the national market, and we knew we wanted to try for a baby, and M wanted as many legal rights as possible in case we moved to an inhospitable state. We got "straight" married in CA in 2008, and moved to MI that year. When E was born in 2011, we were both on the birth certificate, even though there is no second-parent adoption here.
So, to get at your question, I think it does vary from state to state, but that if J were to be legally male and you were to be legally straight married, you would have a very strong chance of having him a legal parent from the start. I don't know how much any of this would stand up in court-- this is all untested law, after all, but I think you'd be safe in all the usual ways outside of custody battles. It's one place where we chose to take the straight privilege and run with it!
Anyway, M is a lawyer and knows more about all of this than I do. But we'd both be happy to talk more about this if and when you need to....
Ok, off to work.