To start it's a Mk-V magnum action. Sorry to say but that action design with the 9 locking lugs doesn't lend itself to great accuracy. To find a factory rifle that regularly shoots .75moa is the exception rather than the rule.

#2. A #4 Shilen is a pencil thin barrel for a .338 magnum the size of the .340 Weatherby. It's pretty whippy.

#3. Get a chamber cast done that includes the full length of the throat and measure the casting against SAAMI maximum and minimum specs for the .340wby. Also measure the length of the throat. Weatherby ammo is designed so that the bullet needs a bigger jump start before the cartridge reaches peak pressure to maintain acceptable chamber pressure levels. If you have a very short throat you could be reaching to much pressure with factory loads which may cause inaccuracies. The throat may also be a little on the loose side causing the bullet to engage the rifling inconsistently from one shot to the next.

#4. Make sure that the bullet is not striking the muzzle brake. I don't think I need to explain this one.

#5. The crown may have been machined slightly off or it could have a ding or burr. Remove the brake and check the crown. Unless he soldered it or pinned it to the barrel it is removable.

#6. This barrel could simply be a dud. It happens. Have a gunsmith look at it with a bore scope and inspect the rifling.