Where did they get the idea that capital punishment is against either Jewish or Church law? The Talmud describes several different death penalties for specific crimes, as well as the Biblical stoning. And if the Church law bans capital punishment, there are a lot of burned heretics who are owed at least an apology.
Then he should be run through a shredder feet first at a feed rate of an inch an hour while a pack of wild dogs chew his face.
Sounds about right to me.