For choosing a wolf rifle I consider a 223 to be too light to be anywhere near ideal.
Standing wolf 100 yards or so, of course, dead wolf. But a running wolf, or at the 350 yards mentioned, which is not really a long shot at a wolf, it's a different story. Look at the ballistics of your fast 223 at 300-400 yards. A high speed 22 calibre bullet falls off tremendously with distance. Look at the ballistics of it out there and decide if that is what you want to use on wolves.
On a side shot if your 223 bullet lands a foot farther back than you intended, that wolf is not going to lay down and die.
I have wounded wolves with each of a 270 and a 30-06, with regular hunting bullets, that required a long follow up. In one case, the only reason I retreived him was because there was tracking snow.
As several have pointed out, a 243 would be excellent as a wolf rifle. But if you have a 308/270/30-06 class rifle, just use it, with your regular hunting bullets.