Once via a sidebar link on r/traa I found a case precedent in the circuit court of Fort Smith, AR which would be relevant for myself involving a court order for gender change without “a certified copy of an order of a court of competent jurisdiction indicating that the sex of an individual born in this state has been changed by surgical procedure..." but instead some other certified medical statement. So far I still haven't found it again in browser history or downloads, but it does seem that "Arkansas Vital Records will accept court orders for name and gender change from other states."