In late January 2024, Barbara Broccoli attended a performance of her stage musical “Buena Vista Social Club” at the Atlantic Theater in New York. The longtime James Bond producer and gatekeeper was joined by three top Amazon MGM Studios executives — Jennifer Salke, Courtenay Valenti and Julie Rapaport — for a night that also included dinner and shop talk. For months, Salke’s boss, Mike Hopkins, had spearheaded discussions with Broccoli about Bond’s future at Amazon. The purpose of the night’s tête-à-tête was for Salke to make Broccoli comfortable with the studio’s loose plans for the first Bond movie since Amazon acquired MGM in 2022 for $8.5 billion. But sources say Broccoli left the meeting uninspired by Salke, a longtime TV executive, and returned to her home in London. Shortly after, talks began for the siblings to relinquish creative control of what is viewed as the last untapped mega-brand, one comparable to Lucasfilm,...