Start by adding a 5mm spacer to the rear. If you get wider rear tires, you will just induce push with the front. It will solve the throttle oversteer, but you will probably loose the crispness on turn-in. It sounds like the car is well balanced but just needs a tiny bit of rear grip. Try lowering your rear tire pressure 1-2 psi as well.
Some might say to be more patient on exit, but we all know that isn't fun at all