Answering the question, "What to do?'--This is not a difficult problem to solve!

I organize and lead a monthly hymn sing(in a religious meeting that has a principled objection to the idea of any sort of leading). with a pianist who is an excellent sight reader, and we've instituted a "60 second rule" which simple is that no more than 60 seconds are allowed to elapse from the end of one hymn to the beginning of another. People in the group call out hymns(and, hopefully, their page number) and sing them.

Of course, this is not all there is to it, there are a couple secret tricks to keep it going--first, though people from the group call our tunes, and all seems spontaneous, I am "the decider" and subtly let George know which of the tunes called we'll actually do next, second, I keep a written out list of the favorite songs of the group, and when their is indirection, I've got something immediately ready so that there is no lag.

Also, when we do a difficult song, meaning one that doesn't work for one reason or another, I move immediately into a favorite. This is important because we have a few folks who call out songs they don't really know, and that are unfamiliar to the group--

I do try to get to everything that is called out, so people don't feel like they've been overlooked, and when new people join us, I make a point of finding something that is special to them, and when possible, I, or one of the regulars will pair with them on the song--

The thing is, I think don't think that the group should just let someone who isn't prepared take control of things, which is really what is happening above--I have three priorities: to keep it moving, to keep it interesting, and to make everyone feel like they are part of things. I try not to let anyone get in the way of that, including myself---