Suppose the controller mentioned Teterboro immediately after the captain had said he was returning to LGA? That would have been a full minute before the captain decided that Teterboro might be the only reachable runway. That seems to suggest Teterboro might have worked if the captain had thought of it sooner.

Would the controller even be allowed to offer Teterboro? Or his he obligated to follow orders from the captain and not challenge his judgment?

I still think the water landing was correct, especially knowing the outcome.