Alpha personalities are often worse performers than they think, and their song choices can be uninspired. Many people (like myself) are very good singers, but having been bred with good manners, we're not pushy--we get short-changed without an explicit fairness approach. Groups should not be dominated by the aggressive, the socially oblivious and the egocentric (as is so often the case).

With a sign-up sheet, you get fairness and the seating arrangement becomes immaterial--no need for literal circles. "Flow" is overrated and often leads to sameness.

If you want your group to be skewed to a few select people, then state that up front and interleave their contributions with those on your sign-up list.