I know that when I listen to "MyTuner" Channel/app, the screensaver will activate the Screensaver set in Roku while still streaming the music/podcast/audio. (This would work with a dark screensaver).
Accuradio has its own's Screensaver with a dark screen, but a little bouncing logo and then cover art. (a little too much flashing probably for sleep).
I am just uncertain if your particular music Channel/app, or any other music Channel/apps will perform in the above mentioned behaviors. (Going to need to test and verify yourself).
Of course, I guess you could also throw a blanket over the TV as well.
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