If you're connected to bluetooth, you should be able to see your messages on messenger regardless of cloudsync or the number sharing settings are turned off. So to me, it might be an Android Wear app issue where it's not recognizing your Google messenger as the default SMS client.
I know it might be stupid to ask but did you check to see if you have the latest Android Wear app, google, and google play services on your phone. When I had issues syncing my old Smartwatch 3, I actually had to install Google play services because it wasn't in my Note 5 for some reason.
One more question
On your phone, what version of Google messenger do you have. I have version 1.8.035. The newest version is the one where they updated it to work with wear for Marshmallow. Maybe the messenger you have installed is different because your phone isn't a Marshmallow device. You did say you have a Droid Turbo right? Not a Droid turbo 2?