Mike,
I have seen the accuracy of a specific bullet change enormously with a change in powder, and also seen the accuracy of a given bullet/powder combination change enormously with a change in primer. But have decided the case doesn't matter much IF it's dimensionally consistent, especially neck thickness.
Have used a bunch of bullets to hunt various kinds of animals from small varmints to 1500-pound big game, and have my preferences. But generally I don't try to "force" a rifle to shoot a particular bullet well, partly because there are so many good alternatives these days.
But I also get to test far more different bullets than the average hunter, and usually have plenty of options on hand--which is why my big game load development often starts with a less-expensive bullet I know should shoot well, such as a Hornady Spire Point or Sierra GameKing, of about the same weight as the "premium" bullet I plan to use. Once I determine what powder and charges the Hornady or Sierra shoots best with, I switch to the more expensive bullet. Most of the time that works--and I end up with both a sight-in/practice/"deer" load and a load for bigger game, which usually shoot to the same place at 100 yards.
