A good knife for killing chickens are the simple stainless steel RADA knives. They are sharp enough to do the throat slit through the toughest skin and they sharpen right back up with a simple knife sharpener. If I am processing many birds I may have to stop in the middle to run my knife over the sharpener a few times but these knives get a good edge with just a few strokes.
I seriously don't think your bird spoiled in that amount of time but maybe your minds were working overtime for you after seeing the fecal matter spilled into this chicken.
I've ate many a gutshot deer and chickens with fecal matter accidents in the carcass and they never had a smell or tasted different....but my dad claimed he couldn't eat a gutshot deer because the meat smelled and tasted like the guts. The rest of the family, without his sensitive imagination, couldn't taste a bit of difference in the meat~particularly my mother, who is the soul of spotless living/cooking.
Yes, chilling the birds in cold water and/or resting in the fridge will make your dining experience more palatable...that is something you should do next time.
As mentioned, a killing cone made from a bleach jug is like a third set of hands. This allows you to place tension on the neck skin of your bird and allows for ease in slicing, keeps the flapping and mess to a minimum and lets one bird bleed while you are processing another.
Another tip....hold your birds overnight in a quiet place and start your butchering in the early morning when you are rested, the air is cool, the birds haven't just been chased and have adrenalin coursing through their tissues, and they don't have so much stomach/intestinal contents in their bodies. This makes the chore much less hurried and frenetic, you are rested and you can take your time and do it right.
