Hey there Travis,.. While I'm not up on the 300 Rem Ultra Mag specs I am familiar with the .338 WM.
I'd personally suggest for you to step-up on the projectiles grain weight,.. something at the least of 200 grains to 220 grain.
Elk are big animals with big bone and lots of thick skin,.. personally I myself would feel a little more comfortable and confident hunting them with something heavier than 165 or 180 grains. I'm using Accubond 220 grainers in my .338 when Elk hunting.