The US fertility rate is less than half of what it was a century ago, and less than a third of what it was 150-160 years ago. European fertility rates are similarly down by fourfold or something. It does not take many generations at all for fertility rates to drop precipitously once child mortality, women's education, etc go up. Your underlying premise "there is significant delay in the abatement of the overproduction strategy if it abates at all" is probably not correct, for any reasonable definition of "significant delay".