The 280 or 280AI will have almost zero advantage over a 7-08 in an 18-20" barrel, and won't even approach a 7mm Mag., considering those usually come in 24" min. The only thing you would gain, is more muzzle blast and flash. The OP's idea of a long throat 7-08 is the best idea of all, but even that will be limited by a short barrel.

As for the reason for the long throat, I am not sure that is the best one. You are wanting to use a "long range" bullet, but with a short range barrel length. If you want a short barrel rifle then do it, forget magnums and forget shots over 300yds at ANYTHING approaching elk size. I would use a Barnes 140gr TTSX and you will get superior penetration and performance within the limited range you will create with the short barrel.

You have specified 7mm, but if you are serious about elk, I would consider stepping up to a 308. Great performer from short barrels, and use a 168gr TTSX and I doubt you will ever recover a bullet, but you WILL recover the animal. Three deer have fallen to my using that bullet and it is excellent, and retains a lot of energy, with a BC higher than most 165gr .308 bullets.

Just my two cents worth.