When I tell my Android Wear watch or my phone to start monitoring, my phone goes to the monitoring screen.
Why not make this screen into more of a nightstand screen. Landscape, very dim (maybe even light reactive using the phones light sensor), something like the screensaver setting within the standard android clock app.
But this screen should be customisable, to show more or less information, such as; time, date, an ongoing sleep graph, alarm details, weather, calendar appointments etc. Maybe different colours too. Different fonts and different sizes of each section would be great too.
I think hiding the notification bar would be the best plan.