I'm surprised that the 9.3x62 hasn't come up yet - is this really CGN?
I'd happily use it for anything in NA. The only stretch would be long range, but a 250gr TTSX (what I use) with a MV of 2600 fps is still at around 1850 fps at 400 yards, which would do the trick if needed. The drop is three feet, though, and the trajectory would be a rainbow by then, but with careful prep and a good rangefinder it could be done.
Of course, I'd take the 270 on a goat hunt, but if I was restricted to just one cartridge I think a good case could be made for the 366 Wagner. I find the recoil no different than a 30-06.