Speaking as a parent of 5. Parental mental health has a much bigger effect on the child than choice of methodologies. You really need to look after yourself before you can look after them - so if you are suffering from sleep deprivation, doing what you have to do is the right thing to do.
Exactly this. Being able to stay sane, levelheaded, and get necessary things done is probably far more impactful than sleep methodologies, baby wearing, breast versus formula fed, or any of the thousand of analysis paralysis inducing choices that parents have to make.
Put your own oxygen mask on first.