I too hunt elk in the Idaho panhandle with a rifle that uses .312 diam. bullets. I use the Hornady Interlock 174gr round nose at about 25-2600 fps with good results (dead elk and deer). The Interlock bullets have always worked well for me in different calibers and I see no reason why your load would not work.
Good luck. It's too bad we will have no cow season up here this year.