"We must ensure "stage 5" is the less-fertile future:"
This is going to be hard without state control over reproduction. So-called spontaneous sub-replacement fertility rates are mean values. Rather than meaning most people have fewer than 2 offspring, in practice it is more likely to imply a bimodal distribution where a lot of people have 0 offspring and another lot of people have 2 or more. This means that in the following generation there is likely to be a fertility rebound as the generation is demographically dominated by those in the high fertility mode.
At least a One Child Policy would limit even the most fertile to 1 offspring only, thus mitigating the above effect.