When I was in college, many of my friends were seriously into archery. They regaled me with stories of the hunts, and the ones they "stuck good" but never found. I decided that stalking to close range shots was a great idea, but I opted for a .44Mag SBH, which shortly turned into a Redhawk in 1984 because wounding game and losing it is not good sport.
I reloaded and practiced A LOT with mild 180 JHPs at around 11-1200 fps. My hunting rounds have always been Hornady 200 XTP's at 15-1600 fps. I've killed many, many critters, and close to 20 Texas whitetail 1-shot bang-flops at distances from 5-60 yards, iron sight. I aim for heart or neck and they don't run.
The only larger game I've taken with the same loads that I felt a little under-gunned were a W. Texas muley (200# -2 shots at about 50 yards) and a 300#+ W Texas Aoudad that a friend hit with in the back with a .28 Nosler at 550 yards. We climbed to retrieve it and when we located it, it tried to get away. I hit it with 4 shots at under 5 yards - shoulder, chest and neck (because it kept getting up) and we too tired to chase it any more! We were caping the ram and my friend reached under the shoulder hide and said "catch!" He tossed me the slug that hit the shoulder bone - knocking him down of course - and stopped under the skin (see below). I would recommend hard-cast or JSP in the 260-300gn range for large hogs, mule deer, black bear, etc.
Forget about .357 or 10mm as a serious hunting round. .44 has unquestioned lethality and the distinct advantage of being available off the shelf virtually anywhere you may go - and that's something that many people don't think enough about.