The Conscience of the Otaking: The Studio Gainax Saga in Four Parts - gwern.net said:
Okada, however, told a story at last November’s AnimEast convention in New Jersey about a strange interlude their studio had with the director while WINGS was still in the planning stages. Miyazaki apparently knew something of their fan work (WINGS co-producer Shigeru Watanabe confirms that his company had Miyazaki look over the four-minute pilot film, THE ROYAL SPACE FORCE, that Gainax made in the spring of 1985 as an outline for their proposed feature film, i.e., WINGS. Miyazaki’s reaction was that Gainax indeed had talent, but that Bandai was going to have to give them a lot of money) and invited some of Gainax’s principle staff over to his home. Instead of discussing working together with Gainax on their anime movie, though, Miyazaki, in the best KARATE KID fashion, set the young men to doing chores, including fixing his roof. Afterwards, Miyazaki brought forth his proposal: he was interested in directing a live-action remake of his 1978 anime TV show FUTURE BOY CONAN, and, having observed Gainax’s work around his house, asked if they’d be interested in working on the film as stunt men. Okada further maintains that months later, during the production stage of WINGS, Miyazaki would often appear in the dead of night (anime studios are busy around the clock) and talk members of Gainax’s crew into leaving to work instead on his own movie, LAPUTA (1986)