Could work as “Children Of Men 2: Cryovault”. In the continuing world devoid of human conception for decades, rare exceptions are insufficient for survival of the human race. A secret embryo freezer is found full of billions of unwanted but viable embryos, and vicious combat ensues to control & distribute to willing - and unwilling - surrogates.
Not exactly how I envisioned it, but that would work very well! Maybe better than what I had in mind.