I've been struggling with this issue myself. I've lost chickens to predators and illness, and know that culling can be much more humane than letting "nature take its course." I've read the pdf of the Animal Welfare Approved website. As a physician, I see the erroneous assumption that "unconsciousness" equates to the inability to experience pain. In humans unconsciousness may inhibit the "conscious" experience of pain - but an unconscious patient can still experience pain and react to it by withdrawal from the source of pain. I love my chickens but I'm far from presuming what their conscious of experience of their world or their experience might be...
Having seen far too many human deaths, I can only hope that my death and theirs is limited to the 30 seconds of experience that the Animal Welfare Approved organization hypothesizes would happen without stunning the animal. To my mind, what happens in the minutes, hours, days or years leading up to their demise is far more important to their humane treatment than the brief seconds that encompass their death.