Ivan,
That is normal. The issue is that under track conditions, the car has body roll (a lot the way you drive :laughing

and that roll angles the outside wheel out at the top. In effect it gives you car some positive camber, which is not only bad for tire wear, but for grip as well. With positive camber, the tire is riding on the outside half.
Your stock Z06 alignment is good for moderate street driving and long tire wear. If you are going to hit the track with the car, it is advisable to get a more 'aggressive' alignment. Essentially, you add negative camber to the wheels (tip the top in) to counteract the positive camber you get from cornering. Tire flex also plays a roll in the wear patterns you see, but it is easiest to think about in terms of camber.
The downside to this added camber is that you will wear the inside edges of the tires more than the outside during street driving. The alignment of a car that is used for track and street use is always a compromise.
Here is my basic C5/C6 track setup. For street tires and moderately stiff suspension (Z06, Z51, Pfadt coil overs, T1 etc...).
Front Camber: -1.3 to -1.5 deg
Rear Camber: -.1.0 to -1.2 deg
Toe: straight in front and rear
This will work nicely at the track and on the street. It isn't optimum for either. We used approximately those settings on the C6Z we ran in the One Lap of America and had good tire wear over 8 track days and 4500 miles of driving. We were starting to wipe out the outer edges of the rear tires due to not quite enough negative camber (we were at -.9 in the rear). We were on street tires and didn't want to compromise straight line acceleration too much (over 600 hp). The more negative camber you put in, the less grip you get when the car is going straight. There are always tradeoffs.
Hope this helps. So just add a little more negative camber and that will even out your wear some and add grip for the next time you head to the track. You should definitely head down to Hallet in Tulsa. It is a really cool track. I think you would like it a lot.
good luck,
Aaron