I didn't build the rifle because of the many points addressed above, and I have gotten much more experience building .308's and other regular calibers. I still want a .375 cheytac in the near future and am planning to use the stiller tac .408. But.... in theory I still think its possible on a savage action (but I don't plan to try it, and don't recommend trying it). Here is why...
585 HE -- Barrels of Cases -- - Long Range Hunting Online Magazine
This cartridge has a rim .654" in diameter and the diameter in front of the belt is the same as a chey-tac and he says he has loaded them up to 65,000 psi, and... chambered them in Savages and Rugers.
So... if that works, why wouldn't a Chey-tac work? Aside from the size of the extraction port. Especially with a Lapua bolt head with lugs that are .050" longer than standard long action ones and the larger barrel tenon. Like I said, I wouldn't try it now after having more experience and wouldn't recommend anyone else do it, but it seems Like if it can handle that cartridge then it would handle a chey-tac. Unless anyone has proof otherwise, I'd think its possible (in theory). I'm just looking for proof as to why it wouldn't work, purely for academic purposes.