I'm a bit direct at times and don't always fully explain myself. In the situation given that you have a wounded animal that is probably flailing/ thrashing and no firearm, back home the general consensus is to go for the neck. You out yourself in too much harms way with the hooves to go for the heart and it's too easy to miss on a moving animal.
Generally it is easier and safer for you to hold the head just enough to get in a good slice to the neck.
HUH ?
You first told us, "I actually DID grow up on a farm and have a Bachelors in Animal Science" Don't you know the Neck in on the back. You have to mean Throat ? I'm just a good ol' boy from Southern By'Gawd Merland and I have done better keeping up here. College really is for parties and sleeping. Animal Science ? That must mean shooting Monkeys to the Moon. Back home must be New Yurk City.