I've thought this through over the weekend. I'll call a meeting and let everyone know we are now lean. Haste makes waste. After the announcement, we'll be on our way. Maybe we'll schedule our first kaizen event next week. Sounds simple enough, we'll just go look for waste and eliminate it. We've got some pretty smart managers, shouldn't be all that hard.
Consider each time you do that one lap in the pool. If you ask 3 people, consider that 3 laps down and back. Work your way up to 3 or 4 laps every week (trust me, your people KNOW 1000% what your problems are). Now the leaders (coaches) can teach the 8 wastes and lean tools in the context of solving real problems. Pretty soon you will begin to develop a spirit of kaizen, where everyone's job is to do their job AND improve their job.
Once this spirit is built, aim this weapon at policy deployment. Aim it at the problems that become visible as you attempt heijunka in your processes or pull. Without the foundation of a spirit of kaizen to go after the problems that a lean strategy will expose, it is like my brothers and I jumping in the water in 1973 to swim the the English Channel. Bless our hearts.