Hi Paul, from what you describe, your weight is probably really centered as you are choking down so far on the club. You mentioned swaying on your full swing. This tip from Jack's Golf My Way has helped me. Keep your weight slightly on the insteps of both feet. This helps center you over the ball, and, helps remind you to keep the right knee slightly bent going back, one of the main causes of a sway. Hope this helps.

There are so many possibilities of what could be wrong I wouldn't know where to start without seeing your swing. However, a great drill that I learned from Tom Watson many years back really helped me learn to stay over the ball. I'm not sure it will help you, but it likely won't hurt to try.

Take a wire hanger and straighten it out the best you can. In one end, form a 2-3 inch diameter circular loop. Now stick the other end of the straightened hanger in the ground opposite of where you would set up to the ball, maybe a foot or so outside where the ball would be at address. Angle the wire from the ground towards you and bend the loop portion so it is parallel to the ground. Basically, you want to position the loop so that when you address the ball you are looking directly through the loop. The loop itself would be about 18 inches or so off the ground with your ball sitting on the ground underneath it so it is seen by you at address directly in the center of the circle formed by the loop. As stated, the other end is stuck in the ground a foot away from your ball so can not interfere with your swing path in any way. It's hard to explain without an illustration, but hopefully you are able to picture it from my description.

The drill is to set up to the ball viewing it through the wire loop. Keep your view of the ball directly centered within that loop from the moment of takeaway, through the time the club makes contact. This trains you to: A. Not come off the ball, and B, cover the ball through impact. If your view of the ball moves from inside the loop to outside the loop during your backswing or downswing, you are moving your head more than necessary. When you can do it consistently on full swings, so that you never let the ball move outside the loop during your swing until the ball leaves, you're on your way to better ballstriking.

But, again, without seeing your actual problem in real life or a video, I am only assuming this might help. It shouldn't hurt though. Try it. Actually, it wouldn't hurt a lot of people to try it.

Hey Paul, with all due respect, my teaching pro has me choke down on the shaft but about a half inch for control.
My clubs have been fitted and setting up with them is not a problem. Getting a good PGA certified instructor is important and I feel that a good one-on-one session or two can help your issues. It is very difficult to help without seeing your set up and your swing. Having a good fitted set of clubs works well also. Again, I would see a pro again.......cheers......it could take more than one lesson....