I can't help feeling, though, that the question of the executed man's suffering misses the point.
As columnist E.J. Montini noted in the Arizona Central column to which I linked above:
The hand wringing that has followed is not for Wood.State-sanctioned executions are a way for society to express its support for the loved ones of the victims. We can all understand the desire for vengeance: "an eye for an eye" was one of the earliest moral codes. We also want the execution to serve as a warning to others who might be contemplating similar crimes.
It's for us.
We pretend to have concern for the murderer, that we want our state-sponsored killing to be humane, to be civilized – as if such a thing is possible.
But we don't want such things for the murderer. We want them for ourselves. We want the killing to be swift and "peaceful" so that killing a person doesn't upset us.
All that aside, we don't particularly want to get our hands dirty.
Lethal injections allowed us to sustain the delicate fiction that our executions were "humane". Now that the tried and tested drug cocktails are no longer available and their replacements seem to produce public relations nightmares for state officials, though, we have to find an alternative.
Other methods of execution were abandoned because too many of us started thinking they were too brutal. The victim's loved ones might not be bothered by the condemned's convulsions or blood, but the rest of us are. The Eighth Amendment was a handy fig leaf to mask our queasiness as humane concern. (Methods like the gas chamber and electrocution also seem to be genuinely cruel, not to mention unreliable.)
So either we need to get past our squeamishness and consider those abandoned alternate methods of executing people, or ...
We could bypass all the questions of suffering and cruelty by adopting an alternative to the death penalty itself.
I've laid out my objections to the death penalty. Twice. The suffering of the condemned as he's being executed isn't one of those objections, but if that's what brings you to the anti-death penalty camp, great.