If we're going to kill creatures like this - and I have no problem at ALL with that notion, I'm pretty well convinced I could personally put a bullet in the head of a remorseless pedophile like the one referenced above and sleep quite soundly thereafter - then let's do it and have done with it. We owe it to OURSELVES not to become monsters, either by deliberately/"accidentally" causing a slow death, or by providing "adequate" security in general population. For all the grim jokes about falling up 5 flights of stairs, if it's not something we can legitimately and openly sentence a convict to, then we need to do a damn good job seeing that it doesn't happen.
Reminds me of the story I read recently. A WW2 German fighter pilot was closing in a straggling B-17. When he got there he saw that it had already been torn up. One engine gone, 2 damaged, half of the elevator shot away, parts of the fuselage ripped open. The tail gunner was dead, and every other member of the crew was injured. The German could see the waist gunner trying to treat injuries, the nose section was shot up, the pilot of the bomber had only recently regained consciousness. Now, the German pilot could have shot them down. He was only one kill away from receiving the Knights Grand Cross... instead he formed up and tried to help direct the B-17 to safety, peeling away only when it looked like one of the gunners might try to take a shot at him. The bomber made it safely home and so did the German fighter.
When asked about why he let them go, the german pilot commented on something his commander had said to him at the beginning of the war. "Honor is everything. We do not have rules to fight by for them, we have those rules for ourselves, so that might be able to keep our humanity."
So, with that and the decision to execute him in mind we are now confronted with the how. For a while I figured just a massive push of diacetylmorphine, but it seems rather perverse in my mind that we kill someone under such euphoric circumstances when they've brought nothing but horror to others. Then as the pendulum swings the other way we get the methods that are arguably vindictive and like that German pilot, we should shy away from, not for the sake of the criminal, but for the sake of our own humanity. To that end, I suggest nitrogen asphyxiation.
The short of it is, you simply remove the oxygen from air the condemned is breathing, either by purging the room with straight nitrogen, or switching his gas mask over from normal air to just nitrogen. There is no noticeable change to the air the condemned is breathing so no aggravating stressors to cause sudden panic and anxiety. There is no air-hunger that is triggered by a build up of CO2 in the blood because they keep breathing normally. Pretty much the prisoner sits down in a room, door closes, and it really doesn't have to be particularly gas tight door like the cyanide chambers, and at some point the air feed is switched. After a few minutes the oxygen has been fully displaced and the condemned simply falls unconcious from hypoxia (an event noted by some high altitude pilots to be sudden, without warning, or duress) and then eventually dies. Unlike the cyanide gas method, all you have to do is ventilate the room with clean air and it's safe to enter again.