I've shot quite a few big bodied, northern white tail with a 35 Whelen. Nothing further than 300. They usually drop like a sack of dirt. Not that I wouldn't use it further, but I usually grab something else if the ranges might get longer.
I use the 200 grn Hornady. Other than poor BC, they're a good bullet on deer sized game; they expand reliably and I would have no trouble using them for a longer range, lower velocity shots. I'd also try the 225 grn Sierras, with which I've also had great luck. Seems the heavier .358 bullets are usually built with thicker jackets, and though they have a better BC, they are not as well suited to expansion at lower velocities on deer sized game.