You will be fine with the 20ga. and the accutips elk hunting. You are essentially hunting with a standard 45/70 load which is more than adequate medicine for elk.
You're firing a 45 caliber (I think) 260 grain slug at 1900 fps. Assuming you get the advertised 1900 fps you will have 2100 foot pounds of KE at the muzzle and at 100 yards you will still have 1500 foot pounds of KE.
Take the 30-06 for back up though. You're gonna be a long way from home and you don't want to be SOL on an elk hunt if you gun breaks.