8x57 improved necked down to .308? What's that one called?

Yeah, if you called it a .30x57 or 7.62x57 that could be confused with the 7x57 case which is slightly smaller. Reading "Cartridges of the World" the 6mm rem., .257 roberts, and 6.5x57 are based on the 7x57 case but the 9x57(.35 caliber) and 9.3x57 are based on the 8x57 case. The 9.5x57 manlicher(.375 caliber) may be based on a slightly blown-out 8x57 case but this case is not interchangeable with the other 8x57 cases.