I can't even comprehend how anyone could tune out constantly-running TV. Just turn it off!
Listening to old TV shows like TNG helps distract me enough to fall asleep.
Have you tried avoiding screens for a couple of hours before bed, and reading books instead? I had the same problem - found it difficult to get to sleep - and I have experienced MUCH better sleep since moving my last hour or two before sleep to some light reading.
Yes of course I've "tried" that, although I think this sortof incorrectly frames what I'm talking about as a problem. I don't find listening to star trek while I fall asleep as a problem. If I read before going to bed I will just stay up all night long reading. Activating my mind by reading a book seems like the opposite of what I'm looking to accomplish here.