Hmmmm - further homework (and maybe some thinking, although some might doubt it) lead me to agree that maybe, just maybe, old @nor-west might have the right idea, with a fast twist (1:7 or 1:8) 6mm Rem. Plenty of case capacity, plenty of donor actions (well maybe a few less given pooh-seventy seems to be flavour of the month just now).
I can't see any reason why a properly set up 6mm Rem shouldn't shoot well.
I'm not a Beretta fan but maybe a Tikka T3 would be a good basis for such a project with good availability of stocks and the possibility of a decent trigger.
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