The more I think about it, I wonder if there si any benefit to AI'ing or Edg'ing your 338. The reason being is that if you go with a non-standard chamber then you have to fireform all your brass. That means at least 200 rounds down the barrel before you can even start serious load development. Why not run a long-tubed 338 RUM and be done with it, saving the wear and tear on your new match tube?
I ran the 338 Ultra in a hunting rifle for quite a few years (I had one of the first in the country) and it really is a great cartridge. The one and only problem is the brass.
Going to the Edge allows the use of Nosler brass and given the same velocity operates at lower pressures.
Yes, the brass life is lower than the Lapua, but I have never had a problem getting 5 firings. Best accuracy comes at relatively mild pressures so I don't see why brass life would be a serious issue??