I've talked to the guy up in Alaska about his round but he was pretty tight lipped.
People are estimating that the 338 Snipetac will get about 500-600 rounds through the barrel before the throat is burned out. That's assuming you're shooting a match with strings of 10 shots rather than say 1 cold bore shot and calling it a day in the case of hunting.
The 375-416 Barrett Improved will probably get about the same. Brass is just going to be a nightmare to form.
For my own personal preference I would say the heck with it and get a 375-50BMG improved. Pac-Nor offers a 1:8 twist polygonal barrel in that chambering and CH4D has the dies. It would be a lot easier to neck down the brass for that instead of having to buy Barrett brass which is notoriously not the best, or try to form 416 brass from 50 bmg... then take another step and form 375 brass from that. I'll take the boost in velocity and the hit on barrel life if it means not dealing with that nightmare.
Klaus H. used to chamber the round in his State Arms Mach V.
https://www.youtube.com/watch?v=oL1vqAZM_Qg Here's him shooting it here.
People with first hand experience with the cartridge were getting 4k fps. I think with modern lathe turned solids like the Warners and modern powders it could probably be pushed even faster.