I don't know why I didn't think of this sooner, but Airtable is a perfect platform if you want to set up a simple message board for a team of people. I built this interface to do just that.
You can post messages, reply to conversations and edit your own messages. One automation and a few tweaks to the settings and you can allow users to edit or delete their own messages, but only reply to those posted by others. Conversations are added to an ongoing "log" with each message so you can easily keep up with any discussions.
