You can't lower recidivism rates unless you change the culture.
Of course, in this case we aren't talking about recidivism. We're talking cold-blooded murder of an innocent person, with firmly established guilt.
If you've got a weasel killing chickens in your chickenhouse, you don't try to understand it, you don't try to rehabilitate it, you kill it. Once you kill it, it is no longer a threat to any present chickens or future chickens.
Vinyl is final. Well, so is Death. At least for the unsaved, should he suddenly get Death Row Religion (most do).