OP, your 270 or your '06 will serve just fine.
I have personally shot over 3 dozen Elk. They die from a decent bullet in the right place.
I very much doubt the elk have any idea what the diameter is.
That being said, close to half of my Elk have fallen to the 30-06. Also accounting for Elk have been the 264 Win Mag, 270 Win, 7x57, the 7mm Rem Mag
the 7mm STW, a 30-338, the 308 Norma Magnum and the 338 Win Mag.
Every Elk I have shot has been taken with Nosler Partitions.
Almost all shots were inside of 200 meters. A couple were approaching 400 meters, one was a full 450.
So far, no lost Elk. As has been mentioned, practice plenty. Get yourself in decent shape, and enjoy those elk steaks!
Regards, Dave.