Speed comes from working at speed so that your brain can begin to process and recognize what's going on.
Race car drivers do not practice driving slowly so that they don't bump into each other. They train to drive fast with control of the car. They push themselves and expect a little rubbing while racing.
In the same vein, you will not get faster by playing slowly and carefully. You must push the speed limit of your fingers and expect to fumble. This is how the human brain works and you will begin to correct the fumbles automatically. Eventually you will stop fumbling and can control the speed at which you play.
Just like a race car driver controls the speed at which he drives..