Given that you struggle with compressing your iron shots, it does not surprise me that you hit your driver better. The driver swing hits the ball slightly on the upswing, so golfers who struggle with a flippy release often hit the driver better than the irons because the driver does not have to compress the ball at impact.
One drill to help you develop the feel of properly compressing the ball with your irons is to hit punch shots. The shorter backswing and quicker overall swing of the punch shot allows you to concentrate more on getting your hands forward of the ball at impact so that you can forward-lean the shaft and compress the ball.
I would have your swings analyzed frame-by-frame with a good swing coach. Watching swings at full speed and even slow motion can be deceptive and not reveal movements in your swing pattern that could be contributing to your poor release pattern.
For example, if you are not maintaining good hip depth throughout your swing, your right arm may be blocked from P4-P6, which requires you to flip the club at impact to hit the ball.
One last point - the time necessary to develop the skill to compress the ball at impact varies widely among golfers. If you have played with a flip release pattern for a long time, it is probably going to take quite a few months of well-conceived practice to modify your neuromuscular pathways so that you can forward lean the shaft at impact and compress the ball.
Good luck!