I am sorry for your bad experience-been there. A couple of years ago I tried to cull a roo with a hatchet that turned out to be dull. That was an awful experience.
I had to cull a cockerel yesterday, and it wasn't easy, that's for sure. I researched how to before I did it, and by following the procedures from the University of Minnesota Extension Service for home processing of poultry, I now have a home-raised chicken carcass in my refrigerator, awaiting its turn on the grill, and the printed instructions have gone into my "All Things Chicken" binder for future reference.
The actual killing went textbook perfect; I made sure that the knife I used was VERY sharp. The bleeding out didn't take long, and the flopping took even less time. Since this was my first time killing a chicken this way, I wasn't holding the head well enough, and I lost my grip on the first flop. That won't happen again.
It is really not mentally easy to make the cut, but it had to be done, and the info I read made it go right, with little pain to the bird. Check out the site I mentioned above. I don't know how to post links, but any search engine should take you there.