I certainly can't think of many particularly good chapter three movies, not even BttF and Jedi; though there were wonderful parts to both of those. (Azkaban doesn't really count, since it's part three of seven.)
I'm not quite sure how that doesn't count. I could maybe see an argument that since that was Cuaron's first movie in the franchise it doesn't count.
If Nolan isn't up to the task I'm sure there's a McG, Michael Bay, or Paul Anderson ready to step in. Maybe Steven Sommers . What's Schumacher up to these days?