I use the same setup you use Console etc, but still needs tmux in two different settings. The first one is the same as your usage of screen. The second one is when I teach: I prefer to have my notes and examples on my screen and my presentation on the video projector, but that when I'm live coding or demonstrating something to my students, I have to do it on the big screen which is behind me, and my neck doesn't like that at all ; thanks to tmux I can easily have duplicated terminals on both screens :).