The pro carpet setups are usually made to rotate extremely well, especially under braking. They have the control to not spin out. Sounds to me that your front end is making too much traction. Try removing the outer ring or two of pins from your tires. Should help reduce front grip and edginess a tad. Add a washer or two to increase rear antisquat (front of the rear arm is higher than back of the arm). You could also try some front toe in, which may help. Though you said you have already tried it- stiffen the front suspension. I would recommend smaller pistons or heavier oil. If you are running a front sway bar, remove that.

When I ran the car on carpet I almost always kept the same setup from clay/dirt, and just put on the smallest spring cups to really drop the car down. I also ran clay compound Proline Ions with no traction compound on them because our track outlawed hard mini pin tires. It was on rails and no one could catch it.