I don’t know if this will work for you, but I had to provide a certified embassy copy of my marriage certificate to my Thai wife, and as you found out the embassy would not certify a marriage certificate from the United States, but they did allow me to create an affidavit and the embassy did certify that and then we sent that affidavit to the ministry of foreign affairs and they put their stamp on it and those items were accepted in lieu of a certified embassy marriage certificate 
We filed for the green card while my wife was in the United States. She came over on a K-1 fiancé Visa we gave up after 12 months because she couldn’t even get an advance parole approved, which was supposed to only take three months and her mother got sick so we abandoned her application for a green card and came back to Thailand. Now she comes to the United States with me on a tourist visa which is good for 10 years multiple entry.