.308 or .35 Whelen would be fine. Moose are not too hard to get close to and shoot once you find them. I steer clear of the Barnes TSX and TTSX. Even call Barnes and ask them. They generally need higher velocity to expand and work well, so you are either limiting your range, or increasing the potential of wounding an animal at ranges past about 300 yards depending on impact velocity. I've seen them pencil through Elk past 350 yards.

A heavier partition on the .308 would be perfectly fine.