For me, it's a simple thing. Give a full hearing that includes a review of all old and all new evidence.
So, tell me, under your theory of jurisprudence how many full 'do-overs' does the loser in a lawsuit get? One, two, ten, as many as he wants? When would anything be decided?
Just the review of the procedure for fairness and applicable law took 5 years and 5 appellate and reviewing courts. Imagine what a couple of factual retrials would have consumed.
Let's be honest. The opponents of Terri's right to die would keep insisting on more trials and more appeals until they finally got the result (further imprisonment of Terri in that awful body) that they wanted. Then, of course, they would be satisfied that 'justice' was done.
My analysis is that we're still awaiting the first hearing of all the new evidence. In a capital case, any new evidence should generate a full review.
You don't get a 2nd chance to get it right after you kill the party involved.