In the past I have use to good effect "tyre softener" from D.Tweeks. This may make the Avons slightly softer and give a little more grip.
Years ago I was taught by a very good driver, he has won Le Mans 24 hours in GT2. to imagine a piece of string attached to the throttle pedal and the steering wheel. So the more steering lock that is applied the shorter the string so less throttle travel.
This equates to, as you start to straighten the wheel up coming out of a corner the further the throttle can be pressed.
I find this method gives smooth fast exit speeds with no oversteer.
After a while it becomes second nature, as I turn the wheel my right foot comes up and as I straighten up it goes down.