Sandwdge,
In your question, you stated the main clue to the whole problem, "Thin shots are usually right of target and shorter than normal." This indicates that your swing is too "shallow" and coming too much on an inside path into the ball. Looking at dimples, taking the tee out will neither help the problem. A possible problem after having neck surgery is your posture is too erect. That can cause your swing to become more rounded than necessary causing and thin shots. Here's an easy exercise you can do at home that will help to re-program your motion. Take a broom and put it across the front of your shoulders with your arms crossed. Stand in the kitchen with a tile or wood floor. Take your golf posture (bent at the lower hios, back straight from tail bone to head), Make a backswing until the left side of the broom is pointing at the line on the tile or wood floor where the ball would be. Now rotate your stomach and shoulders until the right side is pointing at the same place. This will train your body to swing a little more left in your downswing, bringing the bottom of your swing more forward thus hitting the ball first, taking a NY Strip divot.
Now you really know what the broom is used for!