I just spent a couple days down in Southern California training with two of the top 3-gunners in the nation: Barry Dueck and Mike Voigt, both of whom happen to work for Surefire.
These guys are scary fast on the trigger. Part of what makes them so is that they know how to move fast the right way.
Voigt puts it like this. "My eyes are very fast, my hands are okay, my body sucks and my feet are terrible."
What he is saying is that there is a hierarchy of speed and movement that every shooter needs to factor in when approaching a series of targets. Your eyes can move, process and react to information faster than any other part of your body. The next quickest tool in your arsenal is your hands. Working with your eyes, your hands can shift and engage targets rapidly.
You start to lose time when you need to move your body around, such as when bending at the waist to shoot targets that are obscured by cover. But moving your body is faster than repositioning yourself by moving your feet, which is the slowest way to engage targets.
Figure out a strategy that allows you to shoot effectively while minimizing the need to move your feet, and to a lesser degree, your body and your times will improve.