What Frank Said! +1 on the lack of accuracy for me in my Model 70 in 300Win Mag as well.
However you left out one key piece of information. What are you going to be shooting at? Deer size game, paper, or grizzy bears? That definitely has a bearing on using this type and what grain bullet.
As for the heavyweight bullets, I can see a good reason not to shoot a 200gr bullet in a 300Wby......RECOIL! That would likely make a person flinch a little and is way too much bullet for whitetails. I have a 270wby and have had 300 and 7mm Wbys as well. While both of the now traded Wby's liked bullets in the mid to light-heavyweight range....like your aforementioned 168's, neither shot as well as I thought they should even after a trip back to the factory, so, they went on to someone that wanted a Wby more than they wanted an accurate rifle.
That said, as Frank points out the only way to know is to try! See if a friend has some or a will split the cost of a box to try in his .308 cal. weapon. These seem to be doing well in .30-06's at moderate speed.
Good Luck and let us know what you find out