I'm torn about what to do with that channel. I presume it was originally put there so that you didn't have to run a grass edger against the cool deck, as a way of preserving the cool deck.

I want it to drain, but I also don't want to worry about the Bermuda grass (and seed) being in there and causing trouble. Something that packs tight enough that it won't end up in the pool. So I thought maybe decomposed granite fill with a thin flat stone top, where the stones are 4-10 inches in diameter and 1/2 inch thick. I could lay them in like a puzzle I guess.