Two choices in my mind, both already mentioned.
204 would be my pick IF ammo cost is not an issue. It has the legs to get out well past those ranges on little critters. I have seen them used out well past 400m
or
223. But I would not go the 1:8 twist and heavy pills. I use a 1:10 or 1:12 Howa heavy barrel varmint and it shoots the 35gr and 50gr very very well. My longest shot is about 350m and while the rifle is capable of better, I struggled at that point and I no longer have anywhere like that to shoot rabbits so I have used it as a range shooter since.
It might even be up for sale soon. I have not yet decided whether to keep it or not. But I have a few other things I want and that is one that I no longer really use. If I do sell it, it would be listed in the FS section here first.
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