How about a Rem cor-lok 180 or Federal counter part .
My buddy who won't put a reload in his rifle and buys as a rule the best for his needs has shot 4or5 mulies from 80 to 200 with the Rem 165 gn spbt core-locks . He shoots those in his 700BDL because they have given him fewer flyers and smaller groups lot to lot in his rifle for 25 years . Personally Id go to the 180 and find 1 that shoots well in your rifle and shoot that. You also don't need the uber bullet or super loads the 06' killed plenty of deer and elk just fine with boring cup an core plain jane round nose bullets the 1st 60 years it was around.