From a recoil standpoint, in a Weatherby backcountry style rifle, I would avoid the 300 and go for their fast 6.5s or 257. They will be more shootable. The recoil pad and muzzle brake they use work wonders, but those smaller options will probably be more forgiving accuracy-wise. I shoot the 6.5-300 and the 6.5 RPM. The 6.5-300 is less forgiving, and I think it is simply because the whole rifle weighs 7.2 lbs with the scope.
If you want to send the 300 Weatherby, go for it, but I would look at a heavier platform. Probably, the Weatherby apex with a chunky scope is the lightest. I would want to send the 300 Wby.