I'm in late on this one. First of all, sorry about your chicken.
Another alternative for culling is via the old-fashioned cleaver.
You can practice accurately striking a cleaver into a stump and cleave a bunch of non-live stuff on the stump to learn how hard you need to swing. You can even hold a pretend chicken in your other hand to make sure you've got yourself all coordinated.
We did not have good luck with the neck cracking. It's not the kind of thing you want to get wrong, and there are thankfully few opportunities for practice.
Everyone is a little different in how they approach culling. This is just offered as food for thought & another possibility.