.22 Hornet
I knew two fellas who hog hunted for the Gov't in a National Park. The hogs were declared pests and destroying sensitive flora in same. These guys were both locals, and great shots and woodsmen. Their rifle of choice was the .22 Hornet and they shot hogs high in the neck/base of ear as has been described. INterestingly, they handloaded their Hornets with heavier than normal slugs, though I can't recall bullet weight I'm inclined to say 50-55 grains. These boys killed a slew of hogs.
Based on that, the .223 is more of the same thing and would do fine with same skill and ability.
The gov't eventually got involved and issued stainless 30-06's, which my pal immediately declared as to long and heavy, and the ammo too heavy as well.