The 308 is one cal I've not bought yet. It's a fair monster for power out to say 450m so that's doing all your hunting. It's not the worst long distance cal, you can shoot them at modern ranges using electronic targets.
I recently learned the .243 from Tikka comes with a 1/8 barrel twist. That would be a good runner up option as it could stabilize the heavier 6mm bullets
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