Based on your initial description of the problem, my first visualization of your swing is one that is extremely inside on the take-away. With the shorter-middle irons, you can get away with it and as you see you will hit a hard draw with that kind of an approach to the ball. However, when you make the longer swing with the woods, your club gets "trapped" behind the body forcing you to swing over-the-top or outside-in resulting in the slice. Take the club a little straighter back so that at the top of your swing, you could pull the butt of the grip back to the ball with no manipulation...this little self-check will tell you whether your club is getting behind you or not.