"Endless appeals" is such a blatant strawman here. If there is new evidence available (or old evidence that was wrongly excluded), then of course an appeal is justified, no matter how many appeals happened before. Anything else would be mockery of justice.
the system for evaluating whether new evidence is "new evidence" already exists and is not what is being claimed here. read more into the facts and proceedures of the legal system please.
The Constitution is supposed to guarantee us due process of law.
As a citizen, I firmly believe that a legal system that would condemn a man who is likely innocent to die is not "due process of law" in any meaningful sense. Even if you're correct and the precedent is that this is how it is, well then, too bad for the precedent.