I've struggled with sleep problems as well. I've found that a short walk, maybe 3-4 hours before bed helps. Also, I try to take a warm shower, maybe an hour before (though I know you've said this was hard to do). I use these hourly time frames because I've read doing these two activities too close to bed time can back fire.

And then sometimes good old fashioned chamomile tea can help.

As for reading, music, t.v....when I was looking into how to sleep better, these activities were actually not to be done for one of the reasons you mentioned, that it can stimulate brain function. Maybe try some meditation? Though again, I know how tough it can be to get "motivated" when having these problems to begin with.

I wish you luck.