The morning was already hot and humid as the divers jumped off the boat and descended into blue-green waters off the Florida Keys. With them, they carried dozens of living coral polyps, each tiny animal about to find a permanent home on the reef. About 25 feet down, they reached a section of the world’s third largest barrier reef, which stretched out like a rocky moonscape, mostly gray and barren. A few sea fans waved gently with the current, but there were not many fish—the result of half a century…