The song circle, going round the room thing is not for me, I want to play music socially in a way that involves as many people as possible and that means an instrumental session. Most sessions have someone singing at some point, and I enjoy joining in chorus songs and the occasional solo songs, but to get the buzz you need to loose yourself in the music, and for me that means being part of it.
Good luck with your sing around and session I hope you come to some accommodation that allows both to flourish.

All the best PP