With my logic, I can also take an extreme view of what is a person. I could grant "personhood" to a zygote, and my logic would still hold. No person has a right to tap another person's person, and suckle therefrom. We have the 4th Amendment right to not have our person, i.e. body, be seized. If we are pre-born, we also have the right to use whatever organs and state of being we have to try to maintain ourselves. The government can prevent a doctor from aborting us if we have the capability of doing so. If we are so newly-conceived that our lungs are non-existent, it's not any other person's problem - we don't have the right to use another person's lungs without their consent.
My logic leads us to basically the same conclusion as Roe, where "viability" decides rights, only my path prevents late term abortions much more affirmatively. I regret the Supreme Court didn't follow the same logical path, and used the fictitious road called "the right to privacy" to get where I am.
The 4th Amendment doesn't mention privacy, but it does mention seizure. There is no whole-cloth in my rationale.