"My question is if I know that I will never take a shot longer than 600 yards at game. Will 308 do it all? All species?"
Over the decades, I have used the 308/7.62 in numerous types of rifles and at the 600 slow prone, Palma and 1,000 yard lines, and while it is a very accurate, easy to load and quite capable cartridge, I am not a fan of it for "all species" at 600 yards. Will it kill large and/or dangerous game at that range, most likely, but there are more capable cartridges for those animals at mid-range distances and windy days.
With that said, if it was all I had and with my experiences with it, I would maximize its ability and mine to its fullest extent. YMMV