"To give you senses a boost, work with the hanging string, moving without touching it more than a whisper. At the same time, use your heavy bag to practice drop striking with the opposite hand simultaneously. This should "crosswire" your brain a bit so that there is a melding of extreme softness and extreme hardness. When I move with someone to either take balance or strike, I feel for the slightest indication as to where the balance line is and store energy so that at the precise moment I can take balance either gently or by striking. There is a number of shades of power release and sensitivity that must be developed for more subtle and efficient control."
From me:
"Speed comes from relaxation and efficiency (yielding gracefulness / body unity / smoothness). Movement comes from wherever you are to wherever you're going with no preparatory motion. Slower but smoother motion is often more deceptive than faster but jerkier motion. Personally, I think that while a fast draw can be essential in certain circumstances, a subtle/sneaky draw combined with better awareness and tactics can yield greater advantage."