>>toomuc+(OP)
Solution is simple and well-known but requires balls: separate childbearing from marriage politically, and treat it as a full-time job. Institute flat tax charged from all adult population and use it to pay salaries to all women (not "families") with children based on number of children without regard to "quality", variating (guaranteed inflation-adjusted till age of 18) salaries, and taxes, according to the birthrate factual vs desired: increase both if birth rate is too low, until it is sufficient. As simple as that.
Because this will be exploited by the poorest underclass women who will have lots and lots of children to milk the taxpayer (and that's fine!), the resulting market-based salary won't at all be huge.