ELKampMaster:

I own a Weatherby Mark V Sporter .340 Wby. Mag., and I have never observed any lack of accuracy due to freebore, I seat the bullet to just fit the magazine. I have two other friends who own Weatherby Magnum calibers, and they have no problems with freebore. If I do my part, my .340 Wby. Mag. will shoot under .50" three shot groups at 100 yds., and this also goes for a friend's .340 Wby. Mag. I also have another friend who has a .338-378 Weatherby Mark V Accumark, and he shoots under .75" three shot group at 100 yds., and he is not a serious handloader he loads to save money. He also owns a Weatherby Mark V Deluxe Lazermark .378 that shoots under .75" three shot group at 100 yds.

The 300 gr. Sierra HPBT Match King will probably reach the riffling; you will just have to make sure to start at MIN LOAD watching for pressures. The bullet will not fit the magazine, but in benchrest shooting one loads rounds one by one. Good luck.