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what area are you located in?
when we processed the last of ours a month or so ago, a local fella came and learned how to do it himself. maybe you'll have someone in your area.
IMO, the quickest and most humane way to do it, whether you hang them from a tree, stuff them in a cone or toss them in the weeds, is to cut the head off completely, quickly.
we do use road cones, and they are fairly large (one is large enough to do a turkey). the chicken is dead, it's brain is no longer processing or feeling any pain or stimuli of any sort (the second brain perfusion ends=lights out; cut off blood supply, cut off life). however, the nerves will cause it to jump and flop around, thus also splattering nearby items with blood. if you put them in a cone, it will keep them in one place, keep their wings from flapping around or doing damage to the carcass.
we've done it other ways, hanging with twine (the quite often jump off in the racket), tossing in the grass (the blood starts spraying before you can be full rid of them, so you will get splattered), and the cones work reliably and well.
this is all my humble opinion, take it for what it's worth