What or where are the recurring issues or concerns that the team or its customers are facing day in and day out.
Choose one issue, assign a person or small group to explore and get to the root cause of it.
If that need does not exist, "better communication" is only creating distractions.
For example, programmers working on a commercial application don't need to know the status of the marketing campaign.
By contrast, if everyone spends 15 minutes writing a summary, you consume 150 minutes in writing time but, because most people can read (or skim) 10 times faster than they can listen, you're adding only 15 minutes per person (i.e., 1.5 X 10) for a total reading time of 150 person-minutes. Thus, writing summaries is five times more efficient than an update meeting.