If you are going to hunt, quick or "clean" kills are the most humane thing to do. No doubt about it.
However, the ethics of the kill itself doesn't answer the query
Am I a hypocrite? Do I have a conflict of interests going here?
Let's look at how you describe your behavior.
Come fall, I grab guns and go hunting. If I get lucky and draw a big game tag, then I'll do everything that is legal and moral to fill it. In other words, I plan on killing something.
Sounds a bit like blood lust and if killing for the sake of killing is why you are killing, then it is cruel.
So you said,
If I am walking through the desert scrub and a quail takes off, my shotgun will launch pellets towards it in hopes of hitting it. I am going to try to kill the little bird. Jackrabbits? I don't even have to wait to shoot them.
You are shooting jackrabbits because you hate jackrabbits, because your land is being damaged by them, because the landowner has asked you remove them, because you plan to eat them? If you are killing them for some sort of emotional gratification, then it is cruelty, just like when people kill snakes simply because they are snakes, not because they have a rational reason to remove the animal such as the snake being poisonous and in close proximity to and hence a threat to people and domestic animals.
When I explain these views to some folks, they call me a hypocrite. They see a conflict. How could I be opposed to animal cruelty and yet kill animals?
Depriving life because you enjoy killing is a form of cruelty. That would not be ethical as a hunter.
Are you a hypocrit? From your description, it sounds like you are fascinated with the act of killing that may be without a necessary point beyond emotional satisfaction.. After all, if you go hunting, you are going to kill something, right?
The hunters I respect hunt with goals in mind and if those goals can't be met, they don't kill anything and in fact, don't take any shots. Some hunt particular animals. All of them eat the non-pest game they kill, though some choose to fill their freezers with specific targeted animals, such as a specific trophy, either by rack, size, or both. Some eat the pest animals they kill. The pest animals are those killed because they pose a particular problem. They aren't randomly killing jackrabbits on state land because they think jackrabbits are bad. They kill them to consume them. They kill them because the game commission has mandated that they be eradicated for some reason.
Now, if you just enjoy killing but can justify your killing by filling your freezer or working for some state or ranch that needs a pest eradicated, then maybe you can get the best of both worlds. The concept may be a bit weird, but not unethical.
FYI, I am assuming you described your original position poorly - that your choice of words was not actually reflective of who you are.