Nice hand to discuss.

Your overall line is fine.

As far as his estimated range on the river, it's hard to imagine he wouldn't raise any of his sets on the flop or turn.

You gave him few 2-pair combos so you probably removed them as raising hands.

He might have called you down with a flush draw but he might also be a strong player trying to leverage his having position.

To prevent him from floating you and betting the river with any two you need to defend 51% of your range according to my minimum defense calculator.

The question is whether 51% or more combos in your range are better than AKo in your bet/bet/check line. I would think not.

It might be the case if you had bet/bet/bet.

Conclusion

Of check/fold, check/call, and the bet/fold options I think check/call is the best option.