Sling with Screen Off?

Hi all -
I like to sleep with the tv on, and was hoping to use the new Sling app to help with this. The app itself works great, but it disconnects when I turn the screen off. If I leave the screen on, the app turns everything to full brightness.

Does anyone have a good way to turn the screen off while keeping the connection on? I'm using WiFi to connect through, too, if that matters.

Or could it be that leaving the screen on overnight every night wouldn't shorten the life of my phone? It could just be my paranoia.

I'd love any input or tips if anyone has them!

Ivan