If I were you, I would go to Canada before my baby is born, to give birth in Canada, get your wife and your residence card (because your baby will be canadian born) and then if you want come back to your country and return later to Canada.
Your due date is very close to your visa expiration date and I dont know if they would give you an extension to land, if not, you will only have like two months to make all papers after you baby is born. First of all is the well being of your child but I know many women of my country that go to US to have their babies and then return, at least you will be legal residence and have access to health care.
Best of wishes