DO NOT FIRE FACTORY WEATHERBY AMMO IN THAT CHAMBER.
You will have to start with 338WM MIDDLE loads as your start loads.
You may think that a custom chamber to get close to the rifling is gonna make a great shooter in your 340........but I bet it makes diddly squat difference.
The cartridge is SUPPOSED to have freebore for a reason.
I have/Had numerous Weatherby's, still have barrels in 270, 300, 340 & 375, the first 3 have .375" freebore, the 375 has .500".
All shoot .5-1MoA. Sure, not Benchrest accuracy, but no hunting rifle shot in the field can hold .1MoA in those conditions even if capable.
I would throat it properly, and not get fixated on distance to lands.
Even my comp rifles aren't throated to keep bullets .010-.020", some jump is often better on ES/SD anyway, the transition from freebore/throat softens the start pressure spike.
Cheers.