I have a couple of 25's that I reload and use exclusively for Antelope in Wyoming. I love the 25-06 for this and I back it up with a 257 Roberts. Both are wonderful cartridges on thin skinned animals, but are not sufficient to work properly on larger thick skinned animals at range. It is my opinion, after shooting Antelope, Deer and Elk that the issue is the ELK. I honestly believe that the smallest thing that you can use on an Elk is the 270 and it has to be loaded correctly to do that. I would load it with 150 Partitions and stay inside 300 yards, you can use 140 Fail Safe if you can find them and possibly get out to 400 yards and of course the Barnes MXR is good as well.
All of this being said, I would suggest a 270 WSM or a 7mm WSM, put a brake on it and you can shoot off of the shelf for all of it. I have both and they work well on all that you are trying to accomplish.
Good Luck.