I am disappointed Cajun 47 has not responded.
I think my point is valid in that you can load a 30-06 to handle anything a 308 or 270 will do and up past that to even big Africa game.
How versatile you want or need to be should be the ultimate driver. If never going to do a moose or bear hunt, then 270 or 308 is great (though I wold go with 270 if Elk was on the table)
As noted Savage makes lefties and has a very good rep accuracy wise. Not as pretty but then 300 doesn't buy you pretty and pretty does not get you success (give me a good barrel any day of the week over pretty).
AP has no purpose in modern hunt though it might interest the posters to know that AP was the round used 70% of the time for combat issue in WWII in M1 and 1903 models (it was determined they wanted that capability of penetration and humane kills was not their first requirement!). Its documented so not in disputer.
AP also was quite accurate in the M1 and 1903s as it was the better round design wise over the 150 M1 Ball (it also went a long way in machine gun use for area saturation as distance).
So, under 300 yards its a toss up for the game choice for 308 or 270, and if you want to be widely capable its 30-06
A good shot can take down anything up to including grizzly (Leis and Clark shot more than one with black powder guns shooting round ball), but as the game gets bigger (Moose and big bears) then the better choice is 30-06 as it gives you more latitude for success.