^^What you describe would be defined in the stringing world as a wasted movement. In other words, waiting to get over to the trailing clamp, then releasing the string and base levers, then moving it, and then clalmping the string. As opposed to doing what I am doing. I am releasing the trailing clamp while the tension head is releasing the recently tensioned string. Hope that makes sense.
Roger Federer Pro Staff 97 Play test video