I've come to a conclusion that the solution may be somewhat radical.

If coupling is reduced, it should become the norm for women to have and raise children alone, or at least without a male partner. This increases the burden on women, so at the same time the number of children they must support would have to decrease.

This could be achieved technologically, by filtering sperm to remove Y chromosome carrying gametes. As a result, the female/male ratio of newborns would dramatically increase. At the US TFR of 1.66, a 2:1 female to male ratio would be more than enough to maintain the population. Even higher ratios could be imagined, leading to an almost entirely female population.

Social engineering to reach this state is left as an exercise to the science fiction writer.