Go to a drugstore that's doing it around 4-5 in the afternoon and ask if they have any doses left over from canceled appointments. If they do, they should just let you walk in and get it with no papers. There was someone trying that when I got mine and they got told to come back around 5, and I overheard the staff talking about how there are usually several cancellations in the afternoon.

In florida, I know the FEMA stations had signs up saying they were "safe zones" and documentation wouldn't be checked. I think they asked for ID and a cell phone number tho.

I went to one my county health department in Ohio was running, and they did want an ID.

So ones run by a health department may be best avoided, sadly

Unfortunately I can’t say how NC is doing but my state sent out a mass text saying free vaccines today with no ID required.