Me and my dad are thinking about an Elk hunt in the near future and I am considering one of the various magnums. I like the sound of the .300 Weatherby because I would like a cartridge that pushes a 200 grain bullet at fast velocities. I really like the sound of a 200 grain bullet and I want AT LEAST a .300 Win mag for it.
I'd say again you're going beyond what's necessary. My go to rifle for several years has been my Win. M70 in 7mm magnum. I used that rifle in Idaho for elk primarily. 9 years ago just before I moved to Phoenix I used that gun to kill my Shiras Moose using 160 grain Nosler Partitions. The moose was shot at 175 yards. He took a few paces, stopped, wobbled and went down for good just as I was preparing to shoot him a 2nd time. No need, he was dead. This moose just missed Boone & Crockett record book. The bullet was found just under the skin on the offside and weighed in at just a touch over 80 grains. Furthermore a moose's hide is very thick in comparison to an elk and not to mention has hair that is very thick and about 4 inches long.
About 6 years ago on my first Arizona elk hunt, I killed an older 6x6 bull at 280 yards. Again using the 160 grain partition. The bullet hit a little high as I was shooting downhill and exited the animal just below the midline of the offside shoulder. The elk dropped in it's tracks. He didn't die just right away and I used a .45 for a mercy shot when we reached him (that was one tough old bull).
My 7mm has been changed a bit in the last few years and now is setup to be my Coues deer rifle for the longer shots we have for those little deer. So I haven't used it for elk in a few years now and after killing one with my bow this year I don't know that I'll ever rifle hunt elk again.
I bought a Tikka T3 Light in .300 Win. Magnum for my safari. It will surely kill an elk with no problem and has been a favorite of western elk hunters for many years. I would probably shy away from the 200 grain bullets, to lessen the recoil and use a 180 grain myself. But either way it would be a Nosler Partition, Swift A-Frame or perhaps the North Fork version.
The T3 Light is as it's name suggests a lightweight rifle and is a joy to carry for long walks typical of an elk hunt. I was a little concerned with the recoil, but put a Limbsaver pad on it and with that the recoil is really no big deal. It is the typical magnum sharp crack, but that pad does it's job very well as does the Pachmayr Decelerator on my .375 H&H.
Again I've got nothing against the .300 Weatherby, it's just more than I think you need for what you're after. That said, you've got the cost issue of ammunition for the Weatherby. I also have a friend who had a Weatherby rifle in that calibre and he could never get it to group and has since sold it. Just one man's experience I guess, but it's a datapoint, a rather expensive datapoint however.
I guess my longwinded point is whether you choose a 7mm, .300 Win or .300 Weatherby, the elk will go down no problem provided you use a good bullet and place it well.
For years the only two rifles I had were a .270 and the 7mm. Why? Because I was living in Idaho primarily hunting mule deer and elk. If one rifle was down for some reason, I could use the other no matter what species I was hunting. A .270 may be a little on the light side for elk (don't tell Jack O'Connor that however), but I wouldn't hesitate to use it on elk either.