Thanks for the excellent follow up points from Swancott. I'd just add that although it has been common to adjourn meetings to allow the public to speak, the council on which I serve has recently changed its standing orders so that the chairman has discretion to allow a member of the public to speak at any point in the meeting. There is still a public session which is the preferred time for public contributions, but it is now regarded as part of the meeting, with the chairman exercising the power newly added to standing orders to permit members of the public to speak.
The drawback to adjourning the meeting for public contributions is that once it is done, it is not obvious that there are any rules at all, or that the chairman has any authority. You could invent standing orders for the period while the council meeting is adjourned, but it seemed simpler to retain all the normal standing orders, just giving the chairman authority to allow (or reject, terminate, etc) public contributions within the standard framework.