Depends on the barrel being rechambered, but generally a custom barrel is preferred over a rechambered factory barrel for several obvious reasons. But unless the ranges are very long, I double you'd see enough difference in overall accuracy between a rechamber and a custom on elk sized game worry about.
For elk the 375 would be preferred over the 309 unless ranges will be fairly short (here in the west ranges can be very long). Just does a better job of anchoring the bigger bodied game, especially at longer ranges. The 338 #2 and 358 JDJ's are also great choices for elk, and along with the 375 will drop them at surprising ranges. In a carbine I doubt you'd feel the difference between any of them as far as recoil (IOW, less or no more than the 7MAG). I've owned or shot all of them and there's really not that much difference in recoil between them even in a pistol configuration.