Try rotating and re-balancing your tires, if it goes away, you know it was tire related. The steering stabilizer only dampens the affects of the road, it does not control your steering. If you have the stock stabilizer, it wouldn't hurt to go with a larger one, but here again, it has nothing to do with your Jeep wandering on the road. Friend of mine had this problem on his Rubi, and after he bought new tires, it went away. He was due for a set, and I realize that you said you just got your tires, but that doesn't mean that they are perfect. Start with the rotation and rebalancing, and see what that does.