The length of the bullet its speed and the rate of twist determine whether the projectile will stableise or not. This has been known since the 1860s and is encompassed In the Greenhill formula. Speeding up a marginally stable bullet makes it more stable till the velocity drops. You can get good groups at 100 m but fail to find a hole in an a4 at 200 I know this from experience. Conventional cup and core bullets like your winchesters generally give less trouble than hybrids designed for long range or improved ballistic coefficent as they are more compact.
One other thing if the throat of the rifle is a bit worn you generally find boat tail bullets preform worse than flat based ones. Your rifle will probably be best with the normal fodder the likes of Sierra pro hunter or gamekings especially if it's prime purpose is hunting or targetry out to 500 or so metres.
That's my 2c
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