Killing Cones Dilemma

Since I've lived in the US, my husband's family, and later ourselves, have always butchered chickens by chopping off their head with a machete. I have to say that I hardly could complain about the quality of the meat, although all the flapping would sometimes produce a broken wing or two. But this year we've done it differently - we had too many chickens to process by ourselves since we were also amidst a remodeling project this past summer, so we sent our 80+ chickens to our Amish neighbors to be processed. I have to say that the way they processed them was comparable to ours - the end result anyway. Each individual butcher has his or her own work ethics, and so some chickens, both when we we processed them with our friends and when the Amish processed them with their five daughters, were gutted flawlessly, while some weren't. Overall, I am not sure if I was super happy about they way the did it, but then again, only a buck a chicken. Anyhow, what I am getting at is that the Amish used killing cones which they themselves have made out of, as Jacob described it, cutting off the tops of plastic bottles of a certain size. He even suggested that maybe this is what we should start doing.

In the meantime, I've recently purchased Grassfed Gourmet, a book which provides lots of recipes and general philosophy behind raising pastured meat and poultry. Anyhow, the author in that book claimed that when the chickens are killed with an ax, they can't be bled properly (although I think ours are), and that they experience much more stress this way and that affects the meat. I wonder if that is really the case - since our chickens have always been absolutely wonderful, and they are not better when the Amish did them by using the cones. So now I wonder.

EDIT: The Amishes, as well call them, did a pretty crappy job, though.