We just applied for our long stay permits a couple of weeks ago and had the same problem, as we live in a villa zone with no street name or house number. The migration office in Plovdiv wouldn't accept that we didn't have either, despite us giving them copies of the deeds to the house and our electricity bills, but insisted that we get a letter from the Kmet. He was as puzzled as we were and despite going through many documents couldn't produce anything that would satisfy the migration office, so we ended up 'living with the mayor' simply to tick these boxes!
Incidentally, although our EHIC card is valid for 5 years, our Lichna Carta when we finally received it, is only valid for 3 years. We're not sure whether this is because of our ages or maybe because of the uncertainties over Brexit, as it expires in 2020. We're not complaining though, just pleased that we finally got our cards after jumping through so many hoops in the process.