Late to this party but 408 and 375-408 CT brass is readily available. Not that expensive either. Jamison is the manf. May even have sources on dies.
Sierra 375gr MK are also available.
For bullets, ABC in Salmon Arm, BC makes a very nice turned bullet. Not sure what the costs are but likely less then the 50 (which they also make). So bullet availability is both good and bad depending on how you want to think about it.
As for the CT company, I chatted with the owner years back when they first came out and had the same crazy ballistics. Didn't take long before he was side stepping and two stepping around his claims.
Sorry but that type of business marketing is not my idea of fun, especially at these dollars.
If you do contact ABC bullets, ask about their Barnard 408's. These rifles SHOOT. At 1400yds, there is simply no issue hitting with accuracy any govt would want and then some. I never got a chance to plink out to a mile but they did with excellent results.
There are many options now for an extreme range boomer that are far less hassle filled.
Personally, I would stick with the 338 and wait for the Bergers. Then I would go with a 338-416 Rigby improved or even a 338-408CT and go have some fun. Even a 338 LM improved, edge or mystic will get the job done but if building a rig, why not go for more?
As for extreme range shooting, it is more about the scope setup and whether the bullet will go subsonic then anything else.
The big mechanical hurdle is getting enough elevation to reach out that far.
Then you need to see if the bullet will track after it goes subsonic. If it does, then you just keep cranking on the 'UP' until you reach whereever you want to reach.
I designed and had built a mechanical scope base that resolves my elevation issues. I have various small cal bullet that will go subsonic and I have pushed these to long distances.
A 223 to a mile with sub MOA accuracy (you better believe it was a calm morning) and a 6.5 to just shy of 2400yds.
You don't need a real big boomer but they sure make spotting your shots a whole lot easier.
Jerry