RE: 338-RUM 340-Wby or 375-RUM???
If you're looking for something more than a 300 mag class, go for the old standy by the 375H&H and if you want a 40 go to the 404 jefferies or 458win mag.
All of the above, to me at least ,are pleasant to shoot as far as magnums go. I can't say about the RUM's but I've shot 338's ,340Wthby,416 Rem and 460 wthby and found the older rounds nicer to shoot.