Lydia Peckham had climbed one of the taller trees in her family’s apple orchard in New Zealand, strapping a camera to a neighboring branch with a bungee cord and placing herself opposite it. The reason for Peckham’s impromptu jaunt through the foliage was Kingdom of the Planet of the Apes. Unlike the other Planet of the Apes entries, this one would be populated with nearly all CGI apes, one of which Peckham had been asked to audition to play. “When I first got the audition, I thought, ‘Oh, my god, how am I gonna act like an ape in front...