300 Weatherby is a great round, especially if you have one that has much less freebore. All that freebore Aids in getting the bullet started into the barrel crooked, so find a gunsmith that can throat the barrel to fit the bullet seating depth with the round that you supply. I have done this with several other weatherby calibers and have achieved 200-300 fps over the std weatherby chambering and outstanding accuracy. Anyone that has not had a Weatherby chambering without all the freebore is in for a real treat the first time they try it!
I suggest that you contact Pac Nor on this project, because I think that they have a reamer with no freebore and can use a seperate throater to match the seating depth of the bullet that you supply them.
For extreme accuracy, I would not go smaller than a #5 taper and use a muzzle break, also!
Good luck!