I know this is a relatively "old" question, for you, and I'm commenting on it because I just saw it and have a comment that might be of help. I grew up hunting pheasant with my father and older brother. When a pheasant was wounded, it was my job to kill the birds as quick as possible in order to stop their suffering. I was told to grab them by their heads - firmly - and twirl their bodies around until I felt the head come free of the neck, just 2-3 twirls. After killing in this manner or by shooting them, we always hung them by the feet so that the blood would pool in the head and neck.
I kill my chucks the same way now, after having tried other methods, and am always satisfied with the ease of the process and the way I "feel"about it during and after, the speed of death and lack of suffering, lack of bloody mess, and the quality of the meat.
Know this: your chucks would never have lived, however briefly, were it not for the use you have put them to. You have assured that they have lived well, without suffering, and can assure that they receive a death without suffering. You know that all things live and die and that is just the circle of life, the order of things; best you can do is to eliminate suffering as much as possible.
The discomfort we feel, transitioning from "pet owner" to "live-stock keeper" is something we all go through.