We want to ban abortion as Pro-Life, but conservative Pro-Lifers don't want to raise the (unwanted) kid once it's born
This is pretty off topic but I don't know how you could come to this conclusion. Most Pro-Life advocates or organizations are a hundred percent on board for rasing the kids. Most organizations in this camp are huge advocates for adoption and have very robust systems in place to either help the mother get on her feet to raise her child or connect them with a family who is willing to adopt their child.