Under the same iMessage settings, do you have "Enable Messages in iCloud" checked. When you hit Sync Now with that setting checked, does it make a difference?
If you are still experiencing trouble, I would have to recommend toggling switches and a Safe boot. While this may seem like it is no help at all, many users including myself have solved problems by switching a setting off and back on. It does not seem to make any sense, but have seen it happen after a software update where a setting seems stuck. The safe boot does more than boots without Extensions, it also repairs drive and addresses permission errors. The settings I would toggle are:
- iMessage at Messages > Settings > iMessage
- iCloud at > System Settings > your name on top > iCloud
- Messages at > System Settings > your name on top > iCloud > Messages. If this setting is not here, that may be your problem.