And I just realized it today.  My preferred target is always the second arrow, and I normally move just my feet for adjustments.  Well, I just realized today that no matter where I stand, if I throw at the second arrow I tend to gravitate towards the middle dot, usually finishing with my left foot on 21.  I suppose this might help explain why my adjustments often seem to have little effect, and also why I sometimes tend to throw the ball out too wide.  I assume in those situations I'm drifting LESS and hence throwing it with more angle.  Regardless of this, my average has gone up 15 pins so far this year (to 194).  Should I not worry about it now, and just stick with what's been working?
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...nothing is more destructive of respect for the government and the law of the land than passing laws which cannot be enforced.--Albert Einstein

Anything that you do consistently on the approach is not the end of the world.  I used to consistently drift 3 boards to the left... now I don't really drift much.

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"A word to the wise ain't necessary -- it's the stupid ones that need the advice."  Bill Cosby
"Never argue with an idiot. They bring you down to their level and beat you with experience."

It's called "walking to your mark" The brain is a funny thing, once it gets used to doing something it will want to do that way and think it is correcting your mistake of moving. Much like in golf when you see someone who looks like they are aligned up to hit it left, and low and behold somehow the club is routed correct and they hit the ball straight(where they think they are actually aiming. Much like muscle memory, the brain thinks it knows what you want to do! It will take some work, but you can over come this.

My friend had the same problem and he really would struggle on drier lanes. He fixed it by setting down a towel just to the right (he is right-handed) of where he would want to finish at the end of the approach. This way you can't drift back or you will step on the towel and probably fall. You could see him wanting to drift so bad and he would get so close to the towel and look like he was drunk.

When practicing, after you throw the ball look at what board your slide foot finishes and try to make it a consistent amount of drift on each shot (if any drift) no matter where you move. It is something that I pay attention to when practicing and I see that on a tougher shot just a one or two board drift can mean the difference between a split and a strike.

It has worked for the most part for my friend, over time he began walking straighter. He still does drift sometimes but he is much better at walking straight (I think occasional drifting is a problem for a lot of bowlers though). I would try to fix it during practice and not think about it during league until you can fix it, just my opinion though.