I hate this example, because the real question isn't what should I do on the river, but what should I have done on the turn"

Why allow yourself to get to a river where villain was almost getting odds (real + implied) to call? Villain will either stack you on the river if he hits, or he will fold to any bet if he doesn't hit his flush. I see absolutely no value in letting the hand get to the river in the first place whatsoever.

Push on the turn.

I personally will happily call in button's position, depending on pot size, because MP will either fire a blocking bet on the river that I will happily donkishly miniraise (and which gets a call 90% of the time, just to look me up) ORRRR.... MP will check to me, I will throw a value bet or even a push out there (depending on my read of MP) that will be called 90% of the time.

Thoughts?