Before embarking on a career in academia, I took over as GM of a manufacturing firm.  The previous GM was very much a Theory X manager.  As you did, I spent a considerable amount of my time with my subordinates convincing them that our management style was going to change (all but one bought in) and with my first line employees.  I encountered the same "You don't even know what I do" reaction.  My response was similar to yours "You are right.  Show me what you do and tell me how I can help you do it better."  It took just a few months of walking the talk to gain the trust of my hourly employees.  After some initial encouragement, and given more freedom to make decisions, supervisory employees followed my example and enthusiastically bought in to the new way of managing and being managed.  Operational performance greatly improved under the new system.