If you can only run standard kit, i assume that means you are running a gear diff in the front which cant be modified?

I think that is pretty typical of driving a mini with a free gear diff, in that you will need to drive the car pretty smooth through the corner.

However, if the tyres havent been raced in a while you may want to run your rear tyres on the front to scrub them in a bit then swap them back to the rear to see if they come good.

I raced on astro turf once, we were mainly using M Grips, Kit Tyres and HPi x-patterns (xpatterns only on the front). However, these days on carpet we have been using x-press tyres on the rear (dont use x-press rims though, they seem to shatter pretty easy around the edges).

Like sidecarphil1 said, i would probably also try experimenting with weight, although not really sure where to put it. Although i would keep it around the center line of the car and low down. So i guess on in the inside of the actual chassis in the rear.