Carbon arrows are great for compression but not so much for lateral stiffness (think arrow paradox - see video below - and fishing rods). But as long as the barrel is free floated it doesn't matter, really.
My deer rifle is a M11 that has a light sporter weight barrel (in .260 Rem). I put it in a Boyd's Featherweight thumbhole stock and I can do three shot groups that can completely be hidden under a beer bottlecap . . . but NEVER a five shot group. They are invariably 1-1/2" as the barrel heats up. Pillar bedding and glassing the action (and lower "metal - including a metal trigger bow from GunShack) only helped a hair. And that could just be load development or getting the bore worn in.
Certainly beyond good enough for my hunting situations - but the quest for accuracy is never ending.
Review your cleaning methods and try other loadings. You may find one that the rifle prefers.
Carbon arrow pardox in slow motion:
https://www.youtube.com/watch?v=ffw6m1GS-4k
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