Betting the turn and folding to a raise/shutting down to a call is another option. He could still have a lot of mid pairs (probably with a diamond), the bare ace of diamonds, etc. If we're called, I tend to think against most players the river will check through if we're good, but despite that it would be an obvious c/f to any sort of a meaningful bet if we don't improve.

I don't see anything wrong with check/folding either. I may check/call against a habitual floater who will often give up on the river.