First off, you may not want to try and raise the tee-height if you are already connecting high on the face. Secondly, depending on how high you are hitting on the face (like 1/2 inch higher than dead center) you might be actually hitting your club in the true "sweet spot". For example, the Taylormade Tour Burner and every other driver will have the dead center "circle" outline or dotted line around dead center of the driver face. This is merely a target of impact for more left/right impact, however with a the lower center of gravity (higher launch) drivers like the Taylore Tour Burner, the real sweet spot on the driver is actually about a 1/2 inch higher than dead center. This area, created by the lower sole weight, produces the most COR.
I am not writing the above to change your mind about hitting too high on your driver because I also, when trying to target this higher portion of the club face, have often hit too high on the face and sometimes sky the ball on poor swings. It is likely that you are coming in too steep, yes. I had this problem once as well. It helps to keep most of your weight on your back foot at address and to not transfer too quickly to your front foot. I found that when I was really trying to hit hard, I would transfer my weight forward to quickly and would be ahead of the ball before my driver would get there, creating a much steeper angle for my driver. This lead to alot of frozen rope hooks. I slowed down my forward weight transfer and opened my hips a little more during my downswing and this helped alot. Finally, you could do the above too see if it helps and then place the ball about another ball length forward in your set-up. This allows more time for your driver to begin the upward portion of the swing and catch the ball lower on the club face. Hope some of this helps. If not, go see a Pro and ask for help.