I assume you are talking about an electronic tension head. When stringing the mains you could weave the next main. When stringing the crosses you can start to move your clamp. The clamp on the side your going to clamp is not being used to hold the last tensioned string anyway.
The secret to speed stringing is to do it as fast as possible and quality is of no concern. You don't want any miss weaves though or knot that come untied.
I have the ability to drive people crazy, not sure if I was born with it or I learned it but I'm damn good at it.