I respectfully disagree. It's not good for references, overall, to break a promise to a new employer on behalf of a former employer. It's the old employer, not OP, who moved back the launch date of this project.
The old employer had the notice on file. It should have been weighed into their determination of when to launch. It may have been. They may even have decided since OP was so invaluable that no matter when OP leaves they need one week extra to determine who is responsible to cover for OP's knowledge before they go to production. It is unfair to the new employer to drag out starting because the old employer is unreliable.