we can save $$ with "free" school, but I hear u end up paying even more for tutor classes, so it ends up DSS/private may be cheaper. But I think this depends on the school and/or child.
Having 40k monthly saving before sending to DSS/private seems quite alot. I think around 5k monthly saving is enough? but providing there is some savings in bank for emergencies, and that family is still living comfortably (ie. can still cut down on restaurant dinners and vacation if needed)