I've shot several Mk V 240 Wbys and was impressed with both.
As alexkeyser said. if the 300 is shooting well and has at least half the barrel life left it doesn't make economical sense to rebarrel. Having said that, who really cares about economical sense.
I doubt you'll gain much with the 338 over the 300. A good shooting 300 wby will do what needs to be done, with the correct bullet, as far as the load can be shot. Same goes for the 338 RUM. The animal isn't going to know the difference.
Also you may wish to check out the APS 338 AX. The animal won't know the difference but you sure will.