Dan,
My comment on the pliers was based on the information on the Humane Slaughter website.
My view about using a cone or stunning is that it adds a stage to the process and therefore, in my opinion, adds to the stress.
It is my view too, that using a cone is for the person's convenience to avoid wings flapping, and is not for the benefit of the bird, which should be dead by the time the wings flap, so doesn't care. In which case it's not done for the bird's benefit but for the person's because some people are distressed by the flapping. In my view it is not ok to add time and stress to the procedure (and tell me being stuffed head first into a cone isn't stressful) in order to relieve the person's stress. The person should get over it in order to do the best job for the bird.
These are of course, merely my opinions, which I made very clear in my post - note the abbreviation IMHO.