Continuing to practice Woohoojin's overshoot drill. One thing that I learned is that when I flick, I tend to overshoot quite a bit.
Having stronger mouse control and snapping to a smaller distance from the head seems to result in a much, much quicker response time, and when the movement is nearly caught up to the speed of the flick, then it should feel like one fluid motion where the flick and strafe happens simultaneously.
This leads to the "snappiest" flicks, so hopefully I could continue this drill to the point where it becomes second nature.
It's also worth mentioning that this strafe movement isn't applicable in all circumstances. Simply holding angles do not require this movement, however a continuous strafing back and forth is never a bad option when holding angles. Perhaps I just need to play more DM to try the variations out.