In general, if ever there's a liquid spill that seems impossible to clean up, dump some salt on it and let it dry. And when I say dump some salt on it, I mean, grab a can, and pour, pour, pour.
The salt will pull out all the moisture, and once it's dry, you just vacuum it up. Yeah, maybe not too practical to do when you're in labor, but, it works on carpets, furniture, etc. as well, and is really good for pee clean-up with pet accidents.
Then you can spot clean with whatever your preferred stain remover is without having to worry about if it's penetrating the whole way.