Do you think more user and stakeholder engagement would have helped the public accept your research? I have no idea if BPS has the bandwidth for supporting this type of engagement, but I imagine a lot more fears would be assuaged if parents could have some role in "co-creation" of the algorithm, rather than just accepting results.
A lot of research from the fields of citizen science, public understanding of technology, and user experience show that participatory design techniques can enhance acceptance. E.g., https://www.bmj.com/content/319/7212/774.short