I'll second this wrap-around method - it's taught in certain circles as what to do if a dog latches on. On a related note, when I was a kid I also saw a really crusty old desert-rat of a coyote hunter/trapper kill a 'yote in a similar manner, as part of a two-step method of killing a trapped animal without shooting it. It's worth sharing for defense reasons as well.
When he came up to the animal in one of his leg traps he used a hardwood dowel or handle of some kind, and would swing hard right down on the bridge of the coyote's nose, 1-4 inches back from the actual tip. There are so many nerves in a canine right there that the impact caused the coyotes to go from snarling and snapping, to seized up rigid like they were having a seizure. Stiff and vibrating but unconscious. Then he'd straddle them from behind, put one forearm on the back of the neck at the base of the skull, then grab onto the coyote's nose/muzzle with the other and wrench it back, leveraging the skull/neck against the forearm. There was an audible snap-pop, and dead coyote. It was absolutely gruesome, but unarguably deadly.
For me, the most instructive part was actually the muzzle strike. Instant KO. Dogs in a fight can take an enormous amount of bodily punishment without letting go, but that nose strike is the off-button.