[Tom Line]

Do not let air out of the tires. Increasing the friction patch with non-ideal tires that interact with the carpet beyond the surface will only increase traction.

We had the exact same configuration - 4 WD wide with pneumatics. We intentionally put it on the kitbot first because we were worried about turning (having never used pneumatics before), and we found the same thing you did. We changed out to different wheels and went 6 WD wide just to make sure - 4 WD wide with center of gravity centered can still struggle to turn with the wheels at the corners.

Inflate the tires to max pressure to minimize the contact patch. That will help some. Beyond that though, you may need to change your center of gravity (see if moving your batter to the opposite end of the robot helps), or change your wheels.