I agree...with the 338..personally I'd build a 33 Nosler or a 338 Norma... you also do not have a heavy rifle..nothing to take care of Buffalo, elephant ect...I'd also suggest a 375 of some type, or even a 416. if your looking for gaps.
But if your set on building on a origin... 338 RCM...
By the way what does your 30-378 WBY shoot good with? Just curious...
It shoots rediculously good. .5 moa all day with a 168 TTSX at 3550. 80% of groups have been in the .3s with the best being a .122". I wish I had a use to do
Buffalo or elephant but I have enough western US trips planned to last me a lifetime