I coach little league baseball, taught at camps for 3 years, and played baseball all my life. I'm no expert but I think my advice possesses some validity with my background.
My favorite and most effective suggestion for batting speed - Sledgehammer and tire (or tree)
Get an average sized sledge hammer and swing around at a NW or NE angle (depending on which hand you are) down onto the tire or tree. This exercise will really beef up your delts and obliques, which is definitely key to batting. It doubles as great cardio, you'll be huffing and puffing if you're doing it right.
Another exercise, put a 45 pound barbell on your shoulders with your arms over it. Do essentially the same thing as twists for obliques, except practice snapping quickly. Only focus on the oblique that faces the mound. This exercise will definitely aid in helping your bring your shoulders around quicker.
Remember: a great quick swing starts at the legs carries through your body. The initial power that started in your legs gains in strength when it hits your trunk. Learning to make the motion quicker is all part of practicing and muscle memory.
Good luck