EZR,

Every circle has its own rules and variations. It looks like your circle doesn't fit your needs. Look for another or maybe start your own.

I take part in 2 'circles' you could do what you want in the 'song' circle I attend although that circle prefers to have something they can sing along with. The other one I attend is a performance circle and the intent there is for folks to try out material. Others don't (well, shouldn't) participate unless asked.

In both these cases the host/moderator starts and then decides which direction the turns will go. Late comers get picked up at the end of a complete round if they happen to join where the turn has already passed.