I think you have two choices.
1) Stick with the 270 and buy ammunition that uses premium bullets. Barnes-X, Nosler Partition, Winchester Fail Safes, TBBC or Speer Grand Slam. You want a bullet that will hold up to a elk at 30-yards. Many elk every year are killed inside of 100-yards. You need a bullet that preforms well from the muzzle to 300-yards. If you shoot a elk at 30-yards with a ballistic tip bullet? The ballistic tip bullet could blowup & fail to enter the animal? I had my own 270-winchester do this on a antelope at 37-yards. (I check the yardage with a laser range finder after I killed the antelope with a second shot.) I stunded the antelope enough to get a second shot after he jump and ran a few yards. My second bullet held together & killed the antelope. Had that been an elk instead of a antelope? I am sure I would have never seen that elk again.

2) Buy a 338-caliber rifle to add to your collection. The jump from the 270 to the 338 is a big one, but its a good choice. This 338 would be a fine collection to your battery if you choose to elk hunt again? The 338 is a fine choice for other game such a big bears & moose.
There could be one problem with the 338? If you do not shoot it well or if you are recoil sensitive? You would be better off with your 270-winchester. Just make sure what ever rifle you decide to hunt with you shoot it well. DO NOT go out to a local sporting goods store & buy a box of premium ammo & think you are ready to go hunting. Buy some ammo now & shoot it. Find out what shoots well in your rifle & stick with it.