I think that your 350 rem mag with a good quality bullet, barnes, kodiak bonded, northfork...from 225-250grs, would do just fine for hunting griz. The interior bears don't get anywhere near as big as thier coastal counterparts. a 250gr 35 cal bullet @ 2400fps is definately adequate for any griz and probably any brown bear in normal hunting conditions but you might want something a little more powerful if heading into the alders after a wounded bear.