So when I applied for a new card in my new name, I brought with me my marriage license (yay!) and my birth certificate (which, by the way was technically not required based on the directions with the application). If you read the big huge banner at the top of my birth certificate, it says:
Certification of Birth Abroad of a Citizen of the United States of America
Can it get more clear than that??
But, apparently, I may, or may not, receive my new card in 2 weeks, depending on whether they put my file under "investigation".