300 Winnie - I took time to read some of the past posts on this problem rifle - but admittedly not all of them. As a firearms/sniper instructor, I do a fair amount of troubleshooting on various rifles - but I'm not a gunsmith. Here's some questions and suggestions that might help, but it's hard diagnosing these things without getting my paws on the rifle:
1. Have you tried any factory ammo through the rifle? Something with a conventional bullet, not a Nosler Partition, not a Barnes TSX? If not, try some. Am not knocking your handloading, it's simply nice to have a baseline from which to work. A box of factory ammo can provide that baseline.
2. Have you tried any bullets known for their accuracy, such as the Sierra Matchking or Gameking? Very simple, forgiving bullets that respond well to a wide variety of seating depths and powder charge weights. These bullets are known to be accurate in a wide variety of rifles. I'd recommend starting with the 100 grain Gameking. Your 100 gr Barnes TSX is a great bullet and I've used it to take two mulies, but it's not necessarily the easiest bullet to work with. Being soft copper, it will also foul the barrel faster than a conventional gilding metal jacketed bullet.
3. Likewise the brass - I'll second the suggestion to try some factory built .257 Wby brass - and yes I've loaded for the .257 Wby before, including making brass from necked - down, blown out .300 H&H stuff, back in the old days. Get some factory brass, properly prep it, and load from there.
4. When you installed the new stock did you indeed use an inch-pound torque wrench? Same with the scope mounts? It's not mandatory, but we're searching for answers here and we need to eliminate variables.
5. Have you checked it with another scope? One that is proven and known to be good?
6. What's the trigger like? Is it consistent? Most Weatherby triggers are pretty good - but if there's any grit in there, or if the trigger has a harsh pull, it's very easy to produce a wide left-right shift on the target.
7. Are you letting the barrel cool between shots? Between groups? A slim sporter barrel, with magnum charge weights, really heats up quickly and will often start throwing shots.
8. Gently asked... How good/experienced a shot are you?
When my rifles aren't shooting well, it's generally my fault. I've had good days when I've been on the firing line at a match and have shot right up there with the "high master" shooters in the NRA highpower prone game. I've even won a few minor matches. I've had other days when I thought I really ought to just sell my guns and take up gardening. It's well worthwhile to have somebody who really knows their stuff take a turn behind your rifle and shoot it a bit.
Best of luck with the rifle! Regards, Guy