Something else to consider, most .338 bullets have a longer Ogive with the cannelure's set back further on the bullets shank.
This would mean if you seated say a 225gn Hornady to the cannelure in the .300 H&H case, the OAL would be extended beyond the original .300 OAL dimension and perhaps not work through a 3.6" magazine.
Moving to a .340 Weatherby is likely easier and more practical for most people.
John
