.280 for elk
By all means, you can use the .280 Remington for Elk. A lot of Elk were taken with the .270 Winchester with 130 grain bullets, and the .280 is similar.
Personally, I would load a bit heavier bullet, something in the 150 to 160 grain range. Premium bullets are worth the price for hunting big game animals.
Elk tend to be a bit tough, but SHOT PLACEMENT is what counts. If you hit it in a vital spot, it will go down. If you do a gut shot, or in a non-vital area, you have a wounded elk that can travel amazing distances. Using a non-magnum cartridge is generally better for an average hunter, because the associated noise and recoil of a magnum rifle is not conductive to better accuracy in the average hunter, or novice. Unless you put a lot of bullets through a Magnum and get used to it, it is generally better to stay with a non-magnum calibre.
Many people are under the impression that a magnum cartridge is needed because of the hitting power. If that elk is hit in the proper place, it does not know whether he got hit with a magnum or non-magnum. Both will do the job. The advantage of magnums is that they can shoot a heavier bullet at standard velocities.
If you honestly look at the average ranges that big game animals are shot, I think you will find that most are under 200 yards. A survey was done years ago, and the average range on elk was about 124 yards, and under 90 yards for deer.
In my experience, hunting Southern Alberta and South Eastern B.C., (from the Porcupine Hills to the Kootenay River), and having shot over 40 elk in my time, there was only 3 occasions where I had to fire a second shot to bring an elk down. (This does not count a few times I put a finishing shot into an elk to dispatch it.) Of lots of guns to choose from, the one I reached for during the big game season was a .308 Winchester calibre, Ruger International Carbine with an 18 1/2 barrel, loaded with 165 grain handloads. It did the job for me, and I did not feel under gunned.
Chosing a suitable firearm and calibre is a personal preference. I have seen elk shot with everything from a .243 to a .375 H&H. If you hit them in the proper place, they will go down. The woman with the .243 had a 100 grain Speer Grand Slam, put it in the heart/lung area, and then waited about a half hour before following it up. It went about 80 yards, with a good blood trail, and laid down. It was dead when she got to it. It was her first elk.
Let the others have their magnums. Just load a good bullet in the .280, get as much practice as you can, zero about 3 inches high at 100 yards and you can aim dead on out to about 250 and you will not be more than 3 inches high or low from your aiming point, and go hunting.
Take the road that runs west from the north end of the Chain Lakes, and go shoot your elk.