I suffer from the same problem. The slide gets the club stuck behind you, causing an overly inside-out path. First check to see if your clubshaft isn't too flat on the backswing. If it is, you'll need to slide instinctively to make room on the downswing. Make sure your weight isn't too much on your heels at setup- this makes you swing too flat and slide coming down. Get your weight towards the balls of your feet at setup, and learn to feel like you're taking the club just a little straighter back for a little longer (but let it set).
On the downswing, feel like you straighten your front leg ASAP and "spin out" from the top, swinging left immediately. In other words, feel like you're going to hit an over the top pull-cut. I mean, OVERDO it, to the point where you start to hit some cuts. You'll notice that the ball won't pull- it'll just start straight and drift softly to the right. And, your divots will be straight, rather than pointing right. Actually, a good divot is straight with a tail to the left at the end. That's what you want to strive for.
Don't worry about overdoing the pull-cut feel. I've looked at myself on video doing it, and I'm still coming from the inside- just less so. If you do video yourself, strive to look more open at impact, with the clubshaft pointing at the target or even slightly left of it at the last parallel. If your shoulders are too square, the clubshaft will point right, and a hook or push is in play. Soon, you'll start the ball straighter. If it hooks left, it means you just need to get rid of some of that extra clubhead rotation that you had before. In that case, feel like you're "holding on" and not rolling your hands.
This is a better player's problem, and it takes a little time to get rid of it, so be patient and hit lots of balls.
Brian? Redgoat? Anyone? Anything to add?
P.S.- this is a "Flame Ragman"-free zone, please.