I am working on this too.
Here are my thoughts, hopefully some of this will help.
What is your right hip doing? When I am swinging my right hip gets in the way and my upper body is forced to move 'over' it, aka over the top, aka too steep.
The hip motion and right shoulder action is critical here.
I am a swinger and I don't know for sure if the hip action for hitters and swingers are the same. I believe swingers need to slide their hip across the line (sort of out to right field). This move, for me, needs to be exaggerated.
Also, the better players that I know don't have overly long swings. The longer the swing, the harder it is to swing back down correctly. Maintain those flying wedges from start to finish.
The image I like to use or even warm up with is to act like I am going to throw the club out to the target. When I do this, the lower body leads and my head stays relatively still, but I do have the correct hip action (axis tilt). Don't overcook the axis tilt.
When i got a lesson from Ted Fort he told me that he used to play with a guy from Austrailia that was one of the best ball strikers he'd ever seen. The aussie told him that for two years his main swing thought was to keep his tailbone to the target as long as possible.
Jack, in one of books, said that he liked to keep his butt out as long as possible. This is akin to Redgoat's tushline and there is perhaps no better way to 'drop into the slot' than to monitor the tush line. This can be done easily by placing a small a chair up against your backside and swinging. Nearly all golfer, that i've seen, who come over the top stand up and they will end up coming off their tush line.
Where else could you be going wrong?
Well, there's the takeaway, of course. And it's amazing how much money people spend on lessons, clubs, and training aids and what they don't realize is that they are dead long before they even reach the top of their swings. In my experience, when i take the club to the inside too much I tend to be very steep coming down (golf is a game of opposites). Of course it is possible to be at a terrific top of swing position and still come down too steep.
My advice:
1.) Check takeaway
2.) Check position of right hip. If necessary setup a bit closed to the ball and think keep tailbone to the target
3.) let the lower lead-get the weight to the left side first before you swing down.
4.) don't be afraid to shorten the swing some