I don't disagree with anything you said, except for that part. There is no right to privacy in the Bill of Rights. It was that misinterpretation which made abortion a "constitutional right."
This is true. But, one was found in the penumbra (shadow) of the emanation (light) of other rights protected by the Bill of Rights.
In 1965, in Griswold v. Connecticut, (a contraceptive case) a "right to privacy" was found in the penumbra of the First, Third, Fourth, Fifth, and Ninth amendment emanations.
Roe v Wade, on the other hand, was decided on due process. The court ruled that the right to an abortion "is embraced within the personal liberty protected by the (Substantive) Due Process Clause of the Fourteenth Amendment".
(Due Process, not the "right to privacy", was also used in Lawrence v Texas, the sodomy case.)