The beauty of doing A3 is that an A3 team is a group of people looking to solve problems the way his Royal Highness has to deal with us. Not top-down, but horizontally. A typical mission from the King might involve sales working with marketing, or product development. It might involve customer service working with quality and production, etc., etc. Good A3 teams can assemble at a moments notice, and not spend much time in long meetings. Good A3 teams are good at navigating through the DMAIC, leveraging diversity and gaining agreement. And getting back to His Majesty before he expected you to.
It is said that it is impossible to do A3 (or Agile or Scrum) in a hierarchical bureaucracy. Practice doing A3 using employee suggestions as your first projects. People will learn to pick the right team, how to play well together, and how to stay focused on DMAIC (Define-Measure-Analyze-Improve-Control), not DIAMC. Once they get it, you will have an incredible competitive advantage. And the King's approval!