I'm not sure you're understanding Shot Zones, then…
If you're hitting the driver 5-50 yards right, then… you can aim left. You should be aiming left.
Do the woods have a lot of undergrowth on both sides? If one side has trees but is clean underneath, then you can favor that side because you at least have a potential second shot.
I used this approach on the 18th at Trull Brook yesterday. Short narrow par 4. Left is OB, right is the 9th fairway with a few trees separating the fairways, but clean underneath. Usually I would take a 3H or similar to just get it in the fairway. This time I took driver and aimed so my shot zone would not put me OB. I ended up a few feet on the right in the 9th rough, but with a shot at the green.
Remember to slow down your practices. I tend to be too impatient and go to full swings when I should be doing slow repetition. I have a different priority piece than you. But it takes a while to change a habit that we've developed in our swings. It took me 6 months to get my hands higher at A4. Now it is taking me another six to lay down the shaft from A4 - 5.