I was under the impression that the 308 was already pretty much an "improved" profile, with minimum body taper. If you want another 100 to 150 fps, get the 30-06. THAT can be improved with less body taper. And in the Handi action, case length knows no limits. Just ask Mac!!!
Ackley cartridges aren't too slick in break open guns. If they're chambered properly, the factory case will be a crush fit in the chamber and the gun will be tough to close. Too loose and the cases break in half and the accuracy is poor. Best to save the AI's for bolt actions.
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