Your son will not be undergunned or at a disadvantage with an 18.5" barreled 7MM-08. My family has three guns in this cartridge and those little 08's have accounted for many deer, elk, antelope, caribou and coyotes. As stated in an earlier thread, the Barnes 120 grain TTSX is a proven bullet and is our personal bullet of choice in the 7MM-08, no matter the quarry. I would also suggest that as long as you keep Elk distances under 300 yards and Deer/Antelope distances under 400 yards, it will do the job, and do it well. (I actually have loads using this 120 grain bullet in my std 7MM Rem Mag, and for my 7MM RSAUM) Bullet performance is incredible and I wouldn't hesitate using that little bullet on the biggest moose on the planet.
Barnes recommends keeping the OAL to a point where the bullet is considerably back from the lands and grooves. (See their website for details) I have found that each gun does have a sweet spot as it relates to COL. Find it and they will shoot.
For the 7MM-08, each of my guns prefer a different powder... BLC2, Varget and Hybrid 100 V. They will all shoot 1/2" groups.
Happy Hunting and Loads of fun