A flop bet would be a waste here as anyone you want to fold won't because the pot is huge. You have to call one bet back. At the very least you have 3 outs to the gutshot.

The turn is tricky. I'd take a wait-and-see approach. Check, and see what happens behind you. If it's 2 back to me I fold. But it's only 1 so I call. I considered raising but I don't see what purpose this would serve since it will likely drive out only the hands you beat.

I check call the river.

So I play it the same as you.