Fascinating! I tend to have a couple of nights every ten days or so, when I hardly sleep at all, and have had a bit of success with similar music on Smooth Chill radio...
One way I've found is to memorise a difficult crossword clue, and by the morning, it's often solved!
On the other hand, if you wake up very early, try listening to Steve Allen on LBC - he's hilarious, but can also switch you off...