Ken Waters did a .375 on the .303 without increasing the shoulder diameter and did this on a Ruger #1.

I'd be inclined to think in terms of an improved .303 case shape, for the case longevity increase straighter cases are prone to provide and for the improved case capacity & performance in the #3's and #4's.

In a re-barrel, the .270/.303 was popular in Australia for a time and included factory ammo thus head stamped.