I'm toying with starting up a singaround type session in my area (it would be my 3rd try in doing this over the last dozen years or so!) We're kind of out of the way in the suburbs of CT-USA and so our issue has generally been a lack of contributing regulars. All of this discussion is very helpful to me as I contemplate what would be the best format.
   Looking over the original five methods and then reading the subsequent entries ... I'm still sort of gravitating to method 5 (see the following copy/paste in brackets)

[I'm going to put forward a "Method 5", which I don't think I've ever come across, but which might work. It's like Method 4, but with a slight difference. When a singer/player had finished their slot, they then go onto the end of the 'list' again, should they wish to stay and do another song, and anyone who comes in after them has to wait until their second turn before doing their song/tune. This would avoid the situation where someone gets in at the start, sings in front of three people, then has to wait for the whole session, and might get a second turn if they are lucky, whereas someone can come in half way through, sing r to a crowded room, then bugger off. Once again, it needs a good organiser.]

   Around here at non-traditional "Open-mics" lists are generally kept and adhered to. People often play and then leave soon after - which makes me partial to the re-sign up idea stated above.