Thanks for the help. Turns out I was being stupid and I don't actually have BP installed, so I'm not sure why none of my NPCs will give birth, either normally or through the Start_labour command. Admittedly I do have a lot of NPCs pregnant so I'm not sure if that would affect it, but I'd rather they give birth than console end their pregnancies. Maybe I'm just unlucky I suppose.
Edit: One of my NPCs with less days pregnant than the one I was focusing on just gave birth, so I guess its a problem specific to that one? Who knows.