Have a look at the postings by Gleb Tsipursky who has been deeply involved in exactly such an enterprise: trying to bring rationality to much more widespread ("ordinary") audiences through a nonprofit organisation "Intentional Insights".

It is a controversial goal, and he's certainly faced criticism here on LW for the approach he takes. But very close to the main ideas expressed in your comment.

(I am not affiliated with Gleb or Intentional Insights, just thought it was relevant enough to mention in this context)