Building agile teams in a large organization

I went through a successful agile transformation a couple of years ago, and I think I have some idea why it worked so well. 

We focused on hiring people who were already agile, or who had a strong desire to become so.  We then seeded several teams with developer-coach consultants.

To do something similar with an existing organization, you'd have to either fire & then hire a lot of people, or build teams more slowly.  

I think this would work well:

• For any given team, put 8 hard-core agilistas and 2 people who have an interest in it from the existing staff. 
• Every month (give or take a week), add 1 person from existing staff.
• When the team gets to 16, fission into two teams and repeat.
• Keep working your way down to the people who had the least interest in going agile.

That means it would take 7 months to build the first two teams (or if you're willing to bring in 16 contractors at once, the first four teams).  It's a big investment, but if my experience is any guide, it's a big payoff, too.