I decided to implement this change after exhausting myself, day in an day out, with admonitions to "quiet down" every five minutes. If I was doing this every day, several times a day, and it wasn't working then I'd better do something different to accommodate my need for quiet and my students' need to socialize. I found this idea described in the Teacher Learning Center website. It made sense so I decided to implement it.
So what happened today? Even though the children had been given "permission" to talk with each other many of them chose not to and those that did were mostly using quiet voices. It worked this morning but it could have been because the children had already had a chance to talk with each other for a few minutes before I stopped them and introduced this change. I will be observing this situation over the next few days to see if it meets the two needs I identified previously. But for now, I'm excited to see what happens tomorrow.