A few questions - is the 270 what you have and is it something you can shoot well?
You mentioned the 7MM. A 7mm mag would be better, a 30-06 or a 300 mag better still, and a 338 plenty, but if you have the 270, shoot it well, and would prefer not to make a rifle purchase the 270 will work.

Illinois is a shotgun only state isn't it? If so, I can understand not wanting to make a rifle purchase if you don't have to.

A 270 with a proper load will kill elk. I think you should re-consider your choice of ammo though. A better choice would be a 150 grain Nosler Partition. Federal Cartridge makes them. A ballistic-tip might come apart and fail to adequately penetrate on an elk.

There's an good article in the latest issue of Guns & Ammo asking if we're overgunned? The author, Craig Boddington, makes a case for a "yes" answer. In his article Mr. Boddington makes the point that he likes the 338 for elk, but that a 270 will work also. He ranks caliber below shot placement and bullet selection. It boils down to a good bullet that you can confidently place on target.

You mentioned that you primarily bow hunt, so you're certain to understand shot placement. An elk hunt video showed a guided hunt with a 270 wby mag. The elk was able to soak up quite a bit of punishment - 4 shots to bring it down. You were able to see the bullet tracks in the mist/air and the first went into the belly, the second and third were similarly poorly placed, and only the fourth went into the heart/lung area, dropping him. Luckily for the hunter the elk stood there and took it. It it had bolted after the first shot things wouldn't have turned out so well.