Go with the heaviest TSX for caliber you can find, keep shots inside 150 yds, practice like hxll and take only good broadside shots.
Not all elk are created equal. A 250 lb. cow/calf is a totally different beast than a 700-800 lb. bull.

If it were a once in a lifetime hunt that you will traveling across the country to pursue, for a bull I'd go with a bigger gun.

For me its a $50 bill and two hour drive so I have alot less invested in an elk hunt than you will.

Long before the internet me and friends hunted elk, quite successfully with our 30-30s and 32 WSs so it can be done.