The cool thing about strongman movements is that whatever gets the job done is a viable option and should be considered. Of course there are some considerations that need to be made like safety and efficiency, but there isn't really anything that says you MUST lift a stone a specific way.
To follow this up, the type of workout you are performing also dictates how one would optimally move a stone. For example, some workouts are short and are designed to be completed as fast as possible. In this case, a movement with fewer stops and starts/phases would be ideal. On the flip-side, there are other work sessions that are longer in duration and will require more efficiency for the purpose of longevity. You see, performing a large number of reps using a "one-timer" technique or simply just using your biceps more will typically result in some inefficiency later in the workout and possibly even some minor to serious irritation at the elbow.
In the video below, I breakdown how to tweak your technique so as to save those biceps and utilize the larger muscles of the posterior chain to more efficiently move that stone. Before we get to that video, it should be noted again that this technique is not the ONLY technique. There are situations where some variations of this movement are more desirable than others. Play with what works best for you. This is simply information for you to digest and use at your discretion.