By Daniel Wiessner, Nandita Bose and David Shepardson WASHINGTON (Reuters) -The U.S. Department of Labor proposed a rule on Tuesday that would make it more difficult for companies to treat workers as independent contractors, a change that is expected to shake up ride-hailing, delivery and other industries that rely on gig workers. Gig company stocks were hammered on the news, with Uber, Lyft and DoorDash all falling at least 10%. The proposal would require that workers be considered a company’s employees, entitled to more benefits and legal protections than contractors, when they are “economic…