You can never have "too much gun" on an elk that is full of adrenaline! As others have mentioned the .300 is the perfect round for all North American big game. Especially if you hand load, with the variety of bullets available.
I used to use a .300 win mag in a Browning A-bolt exclusively for everything from antelope to elk. Years ago I won a .300 Rem SAUM (almost identical to .300WSM), it has since become my favorite gun on all big game. Nearly identical to the win mag but shorter/lighter and more accurate with my hand loads.
With both guns I have never lost a hit animal in 40+ years of hunting. I have also never had to blood trail an animal - they have all dropped within a few yards of where they were hit.
Shot placement is way more critical than caliber.