With Weatherby's long free bore longer bullets should work fine. Be sure it's reamed to Wby specs. Their factory ammo is designed for that.
I shoot a bit of factory 300gr partition ammo in my Sako/FN custom 375 Wby and tried some 350 Woodleighs years ago. I didn't blue-pill the woodleighs, since my gun is built on an FN Supreme action and isn't as robust as MK Vs. Still, the first Wbys were on the same action that I have.
The 350 Woodleighs were plenty accurate, BTW, even at moderate velocities.