Tottenham, I wonder if you would clarify your question: "On your rear tire do you have a band of wear about 1 - 2 inches off the shoulder of the tire?"
Do you mean where the wear stops--that is how far I am leaning?
Or do you mean a band of greater wear than on the rest of the tire?
If the latter, the answer is yes. That region of the tire has lots of "wrinkly rubber" on its way to coming off the tire.
If the former, I have a "chicken strip" extending about 5mm in from the shoulders of the rear tire.
Why I asked is because riders that do not pick the throttle up early enough get increased wear about 1-2 inches off the shoulder. Its a super easy indicator that you need to be on the gas earlier and usually a little harder. Street tires are a little more forgiving then a slick for this because they heat up easier. Basically your goal is to reduce the time you are coasting, either braking or accelerating. It takes a ton of practice and the key is always smoothness, if you ever feel you arent smooth back out of it by a second and work back up to a pace you can ride smoothly and hit your marks.
You have any video of you riding? Its also very possible you are in the wrong gear and simply dont have the torque to pull out of the corner. If you find your self getting on the gas and having to add steering input to get the bike to run wide, you either are not getting on the gas hard enough, or you need some adjustments to the suspension. That brings me to my next point, if you plan on riding the track a lot get your suspension tuned ASAP. Get it looked at once per year if not even more, as you ride faster your settings need to follow you. The confidence a properly setup bike provides is astounding at any level of riding.
EDIT: Why are you using Q3s instead of the super corsas? Keep in mind that those tires run different circumferences. This means the bike will have a different ride height front and rear, as well as changing the overall geometry of the bike. If the bike has not been setup to run Q3s its even more important to go get your suspension setup.
Here is an example of what im talking about, these photos were taken at the same time. Heres my rear after a day I was struggling to get on the gas on left handers which caused the rear to cold tear and dig a hole into that side:
The right side is much cleaner and my throttle application is much better: