Personally I would go with something in the 150gr range for the .280 and step up to something in the 160gr range for the 7mm.
As has been mentioned, elk do not wear flak jackets, and the time you have to hunt should not dictate the shot you take. Whether it be one day or 100, you should make the shot count by putting it in the boiler room and you will do fine.
Folks have been taking elk with lesser power rifles than your heading out with, many years before any of the so called premium bullets came to be. I would pick something that shoots well, and is affordable enough to get in a LOT of practice with and head off on the hunt knowing you can do your part.
If you shoot one in the ass and it gets away it isn't the bullets fault, its the fool who pulled the trigger. When you COUNT on something to make up for a lack of time or patients, your not hunting anymore your just out to shoot something.
Count on your ability to hit the right place at the right time, if the right time doesn't present it's self, then you still had a great hunt and know that you did the right thing.
When I got my first hunt in Colorado, I went with the attitude that I would do my best to get the job done, if that wasn't good enough so be it, but I would have rather come home empty handed than to have taken a bad or hurried shot and then lost what I worked so hard to find. In the end the elk had moved on from our area, it happens. I passed up several nice bucks as they were just not what I went out there for and ended up taking a nice one with a 24" inside spread, at about 35yds. Great hunt no two ways about it. Not the biggest deer on the mountain, but to me a trophy and he never moved from the spot I shot him.
I wish you the best on your hunt and hope you get it, and get your quarry. Just don't get overly caught up in the bling bling of the latest and greatest thing since sliced bread. Use what shoots the best and you can afford to shoot a lot of. Practice hard from actual field positions and improvised rest, not form a bench.
Good Luck and have fun.