i had the exact same problem - could draw my irons but not the driver. What i struggled with was the alignment of my body and shoulders to the right of the target. Whenever i tried to do that, i would hit the ball in all sorts of directions as i guess my body was compensating for what it saw as a misalignment (i nearly decapitated a guy on the next mat once , earning myself some dark mutterings!).
Finally figured it out this weekend at the range - what worked for me was to align the shoulders towards the target, but take the driver back in a more "around the body" kind of motion than normal. Suddenly, i was hitting draws which started at the target and drew about 10-15 yards , thus ending up left of the target (sometimes it ended up being a snap hook as well, but i guess practice should cure that).
Once, i saw it could be done, it was a simple matter to do the same thing but with the body aligned a bit to the right to the target, so that the ball ended up at the target. I think i hit 30 balls and they were all straight or a draw , which is phenomenal for me because i always faded/sliced my driver before this.
Can't wait to try it out on the course.