Earlier quoted context omitted.
I agree your mind doesn't stop, but sometimes I solve my problems in that moment before sleep, I think because I can direct all my energy to it (even eyes are closed, so no visual processing needed). Though the tired mind is often very keen to simply recurse over thoughts you've already had opposed to think of new ones. If you find you can't stop yourself going over the day though, then 10-15 mins of meditation, wher…
I've found that reading sci-fi/fantasy before going to sleep helps me transition to sleep mode. I think it's because sci-fi problems are really somebody else's problem, so my brain can let them drop when I put the book down.
Seriously, invest $150 into getting a good e-reader, if you don't have one already. It's well worth the sleep benefits, potentially even more than a good mattress (for a programmer, anyway).