I have two 1:12 308's and they both shoot well with bullets all the way to 180 gr. Maybe heavier, too, but I haven't tried them. The only ones I've shot elk with are the 165-gr. Interbond and the 180-gr. Partition.
There are lots of other factory loads that would work well: e-Tips, GMX's, Accubonds, etc. Heck, I think that the Hornady 165-gr. SPBT is good enough for elk.