Tough question with simple answer. As much rifle as you feel you can effectively shoot.

Yes weight is an issue if you are a back country hunter. Are you a back country hunter?? Or is it a guided hunt where you will not be doing alot of carrying of the rifle??

Personally I like the 340 Wby. But I bought mine before the 338 UM came out. I would consider the 375 as the ultimate if you can handle the rifle.

Another question is who is going to chase the elk after you shoot.

I hunt on a 500 foot slide in CO. So I put the 250 grain Sierra directly into the front shoulder. I need to break the animal down instantly. And 250 grains through both shoulders will do that. Does this destroy some meat. Yes It does. But a 500 foot fall down the slide will ruin alot more. And it takes a day and a half to get the elk from the bottom of the slide. Do not ask me how I know how long it takes, just take my word for it. Tom.