I'm in a very similar situation. When I first started using my driver, every shot was long and straight. I just focused on getting my hands around (right over left) so square the clubface to avoid the slice. Then all my shots started pulling and hooking severely.

What I think happened was that at first, getting my hands around was unnatural, and I had to focus on it to accomplish it. Now, it's natural and I was getting my hands too far around. I saw a teaching pro, and he noticed that on my backswing, I was not opening the clubface enough. I was not cupping the left wrist enough. As a result, I was over rotating the clubface through impact.

As I've begun to open the clubface completely on the backswing, my shots have straightened out. I'm still working on having that become natural.

Basically, it takes time for your body to get used to certain motions. When it does get used to it, though, it might reveal other parts of your swing that you need to work on.