There are a few phrases in your description that can give you a clue. "All my shots are lower than others" and "divots with my irons are a struggle sometimes" are a clue that your club ends to be too shallow (too around and parallel to the ground) into the impact area. Therefore when you "put the ball forward and stand closer with left shoulder high" you add to the problem versus ending the cure. As you said, it is a band-aid on the foot when the cut's on the arm. Standing closer and putting the ball forward serve to shallow the good player's approach to impact more leading to thinner, lower shots with the irons and difficulty getting a fairway wood airborne.
The solution? You are on the right track, just going the wrong direction. Get in front of a mirror with a 6 or 7 iron. Bend over at the lower hip joint (where the leg goes into the hip) until you see the club and your spine make a 90 degree angle. This will set your swing on a more steep (up and down) angle which will help the club move into the back of the ball instead of too inside and rising through impact. Your club should bottom out perfectly, sweeping the ground in your practice strokes. As you swing, maintain the pressure i your hips and stay in your (new) posture. That will bring the club on a steeper angle into the ball that will help the ball get more airborne and straighter. Oh and also, when you get this more athletic position, you may just find the ball going further too.