Why not just go with the 338 Win Mag. The 338-06 will get about 90% of the Mag level, but the way I look at it, you can load the Win Mag down, but the 338-06 can only go so far up.
I had a 338-06, never hunted with it, but am now building it into a 338 Win Mag. The power is there if I need it.
Sounds like what you might really want is the Ruger 375 necked down to 338, but that would EXCEED the 338 Win Mag.