I wonder if Godfather Part III might have been an influence on TDKR. Both are action films that are yet quite contemplative, and whose tone is dominated by the pain of their main character. They don't insist too much on the events of the previous film, but at their heart are about the emotional consequences of the journey of their main character in previous films. Of course, Wayne and Corleone are very different, and will end their journey differently but they both start broken by their journey, in almost complete loneliness.
As for inspiration for The Godfather Part III, the second half reminds me a lot of The Leopard: a man, in the very cinematographic landscape of Sicily who tries desperately to protect his legacy. There are long sequences in Godfather III where you completely forget it's a mafia movie, and it's just a contemplative and personal film, like Italian cinema offered in its best years.
I could write for hours about the Godfather films. They were a key moment in my discovery of cinema. This is when I started reading reviews, story about the shooting, interviews, making-of, watching film with commentary by the director. Next big step was watching Ophuls' film, with all their travellings. Afterwards, I rewatched all the films I loved to pay attention to how the camera moved. Since then, I'm a sucker for graceful travellings.