Bigger calibers are not compensation for bad shooting.
A bad shot with a 270 is not going to suddenly be a good shot because you used a 338 Lapua.
Use your 270 and hit where you're supposed to hit. People regularly hunt elk with the 243. It's not a gun issue, it's marksmanship.
I've been on an elk drought as of late, but all that I've killed have fell to a Nosler 150 grain .270 Win or a 180 grain Winchester PP in .30-06. None ran far, maybe 50 yards if you deflate the lungs they can't go very far. Placement of the bullet far outweighs the caliber and charge pusing the bullet. The .270 will do a good job beyond 300 yards on elk and most people don't shoot one that far away unless they are looking for a long shot.
I only know one person who regularly hunts elk with a .243 Win, it gets the job done. I don't recommend it even though it works there are better choices and you have one of them. Another thing to remember is when not to take the shot.