Considering the criteria, I thought the 225gr. SP and 235gr. Speer, driven at 2,200fps would work wonderfully, but voted before thinking it through. To achieve those ballistics, the pressure would have to be very close to 60,000psi, not good for a double rifle.

I think the .405 is needlessly powerful and the big bears, big moose et'al' could be added to the bag, along with most of Africa's game.

Thus for North America, for me, a 7x65R would be better then the rest - even when loaded down to reasonable pressure for a double, it will drive 160gr. at 2,500fps and handle all the game listed - and more. Unfortunately, the factory loads might be too much for a DR, thus the .303 British would be an excellent choice.