My late father shot pretty much everyting in NA including Alaskan bears with a sporterized 1903 in 30-06 firing Rem 180g bullets. Never had to fire a 2nd round due to a miss or a bad hit, all with a salvaged Lietz 4x German sniper scope. Never had to take a shot past 300y either.
My vote would also be for 7mm-08. People use that cartridge for 1200y LR competition and hunting is usually a lesser requirement.
It seems that today people often try to make up with power what they can't do with their own shooting skills. At the end of WWII in Europe my father was hand picked by General Patton to be a member of his occupation forces command as a hunting companion (one of a few). Not only was he not an infantryman (Signal Corps sergeant) but he served in a different US Army Group not even in Patton's chain of command (he didn't even like Patton).