Is there any way to get the screen to turn off automatically while in Exhibition mode?

I typically watch video on the TP docked on the Touchstone at night before bed, and I usually fall asleep while watching. When I awake I've find the screen has been on all night. I don't want this to happen, I want Exhibition mode to obey the auto screen off settings and shut off the display after a set period of time.

Is there any way to do this? It seems really bizarre that I can't find a setting for this.