With the factory guns and barrels it is all a roll of the dice if you want anything close to .5 MOA.
Some will make it, but dang few as a norm. Do not believe the "once in a lifetime 3 shot group one hole group" that always shows up on the internet. At BR central, they have had standing bets for a .25 factory gun to shoot in the short range BR matches and agg .25 for five shot groups and no one has won any money yet.
If I had to try for consistent "tight" in a factory, I would go with heavy barrel savages and for hunting in the 300 WSM
. In fact take the Savage 308 FTR for $925 and rechamber to WSM for another $150 and $20 for another bolt head. Comes with 30" barrel so you can leave it or cut it off to 26". The savages have a much better track record in the accuracy dept over the stock Remingtons.
In reality, you are really talking a custom gun in my opinion in a variety of calibers to include the 270 weatherby. You would be money ahead and happier to rebarrel you 300 Win with a custom barrel and proper bedding and trigger tuning. Dan Lilja shot dynamite shoots at 1000 plus yards with a 270 weatherby so it can shoot.
Also, even then it is a matter of your reloading and bench skills, regardless of how accurate the gun is "capable of".