Depending on how hot you shoot the round is the determinig factor of case life.
Use the Norma cases and load the 30/378 with medium loads. The cases should last you for many firings.
Speed not only kills accuracy (in most casses) but it also kills the case life.
When I shoot my 338/416 IMP with real hot loads, I get two firings out of new brass.
When I shoot it sensible and reduce the load by 5 grains, I can fire them 10 or 12 times and more, without problems.
In my 30/378 with a 36 inch barrel, I use a 220 gr Sierra bullet and a medium hot load and can reload the cases at least 12 times.
If you rebarrel my suggestion would be to go to a long barrel (36") in the 338/378 and shoot the 300 gr Sierra MK. Please make sure you have a Muzzle brake
installed on the new barrel if the whole outfit is less then 20#.