In Ginger Baker's video, he insists that clean strokes at moderate speed will sound much faster than they really are, so you will in a sense pick up more speed by being clean than by actually trying to be faster

Also, a great practice pad is to take an old (but functional) snare drum, fill it with crumpled newspaper, tighten the heads to your normal tension, and release the snares - it's not so loud and can be made to have exactly the same feel as your regular snare - and you can hear the cleanliness of your strokes much better than with a normal snare drum