I get the impression there's a definite difference about songsheets on the two sides of the Atlantic. It's common enough for a singer to stick a sheet with the words down on the table, or open up a folder - but handing round the words to other people is pretty well unheard of. (I mean before singing - if someone wants the words after it's common enough for people to have a spare copy to hand on.)

Maybe it's a question of what makes people feel embarrassed - having the words in front of you is embarrassing here. Maybe it's the other way round over there. (I'm reminded of what seems to be a simlar difference about closing your eyes while singing - Americans seem to see that as a bit unnatural, and done for effect, whereas here it's keeping them open that tends to feel like it's done for effect.) People seem to enjoy picking up a chorus even of an unfamiliar song. And singing along with the verses is a bit frowned on, though it happens with well known songs.

Most sessions tend to have an emphasis one way or the other - they'll be tune sessions with the odd song, or singarounds with a tune now and then. The idea of running two seoparate sessions makes a lot of sense. Maybe you could have them so that, in the song ones, there's a break half way through for a jam, and the other way round for the tune sessions.