There were many, many wildcats based on the full length H&H case merely 'improved' to one degree or another. Since the shoulders are not radiused, I am going to guess 300 ICL Grizzly or 300Ackley. If it were my gun I would merely neck size the cases, shoot it and call it whatever I wanted. Say..... the 300 Claiborne sounds kinda cool, as does the 308 Safariman!
