Exactly. Therein lies one of the problems. Unless the criminal has been charged under federal law (which in fact there shouldn't be federal laws for murder, etc. if it doesn't involved a federal official) the issue is up to the separate and sovereign states. The case should have stopped at the state's respective Supreme Court
I don't think there are.
You apparently haven't heard about the incorporation clause of the 14th Amendment that requires that federal protections also apply to the states. The overarching result of the Civil War and of the subsequent Amendments was to largely abolish the distinction between state and federal. Indeed, Lincoln even tried to justify the war by claiming that it wasn't the states that gave rise to the Union but that the Union gave rise to the States.
You are dead wrong.
U.S. Constitution Article 6 -- This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
U.S. Constitution Amendment VIII - Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.
U.S. Constitution Article 3, Section 2 - The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution.
This case was brought to the Federal Court, by a citizen of the United States claiming that the manner of death proscribed by the State constitutes cruel and unusual punishment, and thus prohibited to any State by the U.S. Constitution...the Supreme Law of the Land.
The Supreme Court has Constitutional jurisdiction over this case.
Your argument would in fact set up a situation where a State could freely violate a citizen's Constitutional rights under the guise of State's Rights...no State has the right to violate the Constitutional rights of its citizens.
You're forgetting the 14th Amendment. States haven't been sovereign since the Civil War.