I have used every method discussed here. All will work, especially on an elk. The key is PRACTICE. That said, I would not give up a ffp mil reticle with exposed turrets for any reason. That scope can execute every single strategy out there, including the best one, dial elevation and hold windage. If you need to use a different method because of speed, you can do it with that scope. Also, for the mpbr guys, I walk around with my scope dialed .5 mils above my 100 yard zero. 0-300 yard shooting at anything deer sized or larger becomes point and shoot with a fast caliber that way.
If you spend a lot of time shooting under pressure, such as on a timer or in a match setting, you get quite fast at dialing a turret. Most people that are very practiced and have great target acquisition skills can dial a turret faster than they can find the correct mark in the hold-over part of the reticle. That said, a ffp scope with a mil reticle and you can hold over if the situation calls for it. Make a first round hit and the elk runs 50 yards and stops, hold .4 up and shoot again. You never have to take your face off the gun.