@realjohnboy,
I am opposed to Congresses and Presidents committing future Congresses and presidents to actions that they were not willing to do on themselves, so I would oppose your timeline.
at first blush $9.70 seems to be in the right ballpark.
I would do it all now, and give states with a low cost of living an extra year to adjust, under the theory that the new higher min wage would cause the most destabilization in states with the lowest cost of living. If these states decide to stick with the rest of the nations timeline fine.
EDIT: these states with low cost of living tend to run R, which I see as a benefit to getting such a law passed.