And no "King and I" ? You aren't sci-fi dorky enough to clobber for not watching "Westworld"..
The big thing was the similarity (both physical and characterwise) between Yul Brynner's Chris and Neal McDonough's Cane in Tin Man. It was more of an `oh, they did that same thing in this other movie' and `oh, that looks like this other present actor' than seeing the same actors in later films.
The closest I've come to seeing The King and I is Jodie Foster's non-musical remake Anna and the King.