Their $33 million helicopters are new. There’s an aircraft-carrier briefing room with their name on the door now. And they get extra parking spaces on the multimillion-dollar real estate of the carrier flight deck. All the attention feels a little odd, Navy helicopter pilots say. “We’re not used to being the story,” said Cmdr. Ken Strong, executive officer of HSM-77, a San Diego-based squadron of MH-60R Seahawks. It’s a good time to be flying helicopters for the Navy. Long in the shadow of the jet jockeys — no one has ever made a movie about the rotor-blade community with Tom...