Yay! The board of Elections relented and faxed me a ballot. I checked out the information on each of the candidates so I could make informed decisions, and then I faxed in my ballot. We are luckier here than at some posts, in that we have APO (military postal service) twice a week, so I will actually be able to get the ballot post-marked in time (they require you to mail the original for auditing purposes. So insha'allah, my vote will be counted.
I was especially glad to get to vote for a guy who was mayor of Carrboro, the town next to Chapel Hill, for 10 years and was one of the state's only openly gay politicians. He is running for the Board of Commissioners, and still lists improving opportunities for LGBT folks as one of his priorities.