You already have the .270 Winchester (which is the minimum caliber that can be used here in Kentucky). It will work fine...Invest in quality ammo witha premium 150 grain bullet...think Nosler Partition, Swift A-frame, Hornady Interbond, etc. Stay away from 130 grain loads and fragile bullets...also avoid the Winchester Powerpoint, Silvertip, and the Remington Core-lokt.Consider looking into the Light Magnum loads.

The .300 would give you more horsepower and the ability to consider more oblique angles, but from my experience, any of those bullets will exit an elk on a broadside shot...not sure of how much more horsepower the ground on the far side needs...