I have the BAT 21mm rear bar with the BAT suspension kit, and I have no oversteer problems at all. I also don't have any real problem with understeer either. The only thing I have found that will get you out of shape is trail braking at fairly high speeds (losing my front brakes at 90+ MPH into a turn at IRP).
From what I have read on CEG you may have issues with the stock swaybar mounts failing over time. I would guess that if your car has been driven through the winter (i.e., the underside is fairly rusty) you are more prone to failure. You may want to consider altering the mounts to prevent against failure.
I would recommend dumping the stock suspension for the BAT kit (or other reputable brand), and I think you will notice a substantial improvement with the way the car performs on the track.
