You're asking a lot of that bullet, given the variety of game you propose.
Typically in the .308, 150-165 grain bullets are best for smaller big game (deer and pronghorn), while 180-200 grain bullets are best for larger big game (elk and moose).
Use too heavy a bullet on smaller big game, and it's liable not to expand reliably enough to perform well. Use too light a bullet on larger game, and it's liable to expand violently, but not penetrate as it should. While it might seem a good compromise to split the difference at about 165 grains, my own experiences (albeit in a .30-06) have shown that 165 grain bullets can display the faults of both extremes, sometimes without any of the imagined benefits.
I'd recommend you look for a 150-grain load for deer, as well as a 180-grain load for elk. This is where reloading is so beneficial. Nonetheless, there are plenty of factory-loaded options out there. You might be surprised how many deer and elk fall regularly each year to "non-premium" CoreLokts, PowerPoints, etc. Don't overlook them simply because they're not "premium".