Don't worrry about the 350gr Hornady not downing a critter in NA, (while the swift,hawk, kodiak, rhino, woodleigh, Northforks, etc are better bullets) I've downed Moose with the 350gr RN and FN Hornady and it works just fine. An friend of mine who is a custom ammo maker uses them in his ammo and he has had nothing but great results on game with them, hundreads of reports on deer, elk, hogs, etc. The Remingtons are fine aswell if not pushed too fast, ie over 1700fps. Again it depends on what your hunting and what you want from a bullet, don't expect a 500grain solid to down a blacktail any better than 300grain hollowpoint but don't expect that sane 300grain hollow point to penetrate an elephants skull or a moose end to end. Match you bullets to your intended game. A 350 grain bullet at 2000fps is a good all around load for anything in NA. A 300gr Nosler Partition, Barnes XFN, Speer Unicor are also great bullets for large NA game.
Good luck.