Ok, the stock setup is great for pavement but carpet has more front grip. Actually more grip over all but if your car is setup for pavement, it will oversteer on carpet. You can start with stiffer springs all around, stiffer front stabilizer, less sauce on the front tires and higher roll center in the front end.
Notice that all my suggestions are in the front of the car? That's because the weight is moving forward when turning. If you follow the weight, you will see the problem.
If you have a smartphone or an ipad, I would suggest getting the RC Workbench app from Martin Crisp. I learned a lot from that app. (shameless plug) Oh yeah... Droop can have a dramatic effect on handling especially in high grip conditions because acceleration and deceleration are more pronounced.