And addressing the Constitutional precedent, I apologise for the legal mind-bending which follows, but I'm amongst other things a Constitutional Lawyer (I've written entire Laws and interpretations which establish primary axioms for Judgement in three different Jurisdictions - UK, as part of the Beta Tester team for the Legiislation.gov.uk online Statute Law database, Belgium, long-term mental care and financial procedings in charities, Albania, restabilising the economy after the pyramid banking collapse). If you need, skip the next paragraph, I only left it in for the formality of the argument.

The entire Constitution is predicated on the primary foundation of LIFE (liberty and the pursuit of happiness, albeit not happiness itself, in the Declaration of Independence which the Constitution impliments). The Constitution opens "We the People of the United States, in Order to for a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America." In other words, the foundation document is the Declaration, and the Constitution an Implimenting Codicil thereto. The two are inseparable and must be read together. If the case were otherwise, then the Constitution would be void, refering to something undefined.
As these cannot subvert themselves, such an implicit interpretation is wrong in Law. If it were explicit, then it might be a legal incoherence, the Law is riddled with them, but an implication is not, it's simply a putative and therefore secondary application of Law and is bound by the primary texts.

In plain text, an interpretation is case law, and bounded by and must be coherent with primary law. The Constitution impliments the Declaration of Independence, which establishes that Americans have a right to life. Any interpretation of the Constitution must therefore defend that, and so your argument falls. A similar provision has recently been built into the European legal structures, more explicitly interdicting any such subversion of the right to life, in the Charter of Fundamental Rights.