We mentioned r Elchonon here who followed in footsteps of Chofetz Chaim in evaluating grim reality of 1900s … interestingly, Chofetz Chaim repeats in his letters again and again about danger of sending kids to wrong schools and a need to have at least one kosher cheder in every town. I saw him specifically naming two treif groups: yidiishistes and tarbut, cultural Hebrew school. I don’t see Mizrahi mentioned. Did I miss it?
Incidentally, his definition of a kosher school: learning chumash with Rashi without skipping any psukim. Double check whether your kids didn’t skip Dina or Tamar or Timna or gemora that doesn’t advise full time learning rashbi style