the OP is wanting to amend the birth certificate. The courts order that would allow that would be from the court that approved the name change. As to the gender change; the form says: certification by medical attendant or affidavit and one document. I suggest OP contact the office of vital stats to find out exactly what they need there.
file:///C:/Users/Jeff/Downloads/vs170.pdf
Now, unless you are suggesting that anybody born in Texas cannot amend their birth certificate unless they remain a resident of Texas, I don't see why there would be any concern of residency.
my rant:
how do the facts at the time of birth change? You are born what you are and your name is what mom or dad put on the BC. That never changes. Now, I can see a correction if there was an actual error but to somehow change the facts surrounding the birth? Seems like a birth certificate is meaningless.

