heavy lifting is great for strength but again you want to train the fast twitch muscles that only engage in a fast start position. Like in my description of pin presses, it's the starting point and the speed of the push that matter in the lift. Training on a bag or pads is great or even doing push ups and shadow boxing with bands.
You have to understand it is an entirely different set of muscles you are training. Sprinters run for short sprints as do hockey players. If they train cross country it will actually hinder their performances because they are working the larger strength muscles and the stabalizers instead of the fast twitch muscles.
Also work speed bag and focus mits for hand quickness, rythem and accuracy. Double end bags are good for body movement. Having a good sparring/training partner helps too.