Great idea, especially your clear, bold articulation of an issue in the first paragraph. Feedback loops (e.g. stories and metics) that share the broader impact of projects could be very useful to cross company lines too and also to help educate people involved in similar initiatives.
Maybe there is a way a more diverse group than normal (e.g. those with lived experience of the area or sociologists) could provide critical input into the design of the project and review of potential impact - to really connect the teams involved to the people involved or who could help make it a better impact in a effective two way relationship.
Projects can move from one company or team to another, and people do try to think about impact but only that which can be easily measured by a 'tool'- be good to continue that focus on education and challenging existing behaviour too. Maybe a general campaign here could be of use. I'd also suggest being wary of binary assessments of good or bad impact - perhaps we need one that doesn't shy away from detail, to account for all the various scales of real-world impacts.
Keep an eye out for other projects coming through from other teams - maybe there is a way to work together, with one group focusing on the how the independent certification could work and the other focusing on the education and sharing learning?