Steering stabilizers, really don´t help much, keeping the vehicle going in a straight line. They do help bumps and road surface changes being transmited back through to the steering wheel. More noticeable with taller tires. Unless they show signs of leaking, I don´t mess with them much.
Maybe if we could figure out what type of shock you have, (go look at the side and read the stampings), we could recommend something a little softer. Have heard good things about Doetch tech. Near stock spec.s but off road worthy. Gas shocks are mostly some stiffer. My Koni´s are valved to help with sway, compress a bit slower, rebound slower. Can get some wheel hop under the right conditions, but fairly predictable. Not harsh, but solid. Of course if the vehicle isn´t swaying much, the passenger most likely is, if he´s not used to it. Never tried Edelbrock shocks.
If your not used to a high center of gravity, that side to side motion can be strange. Gets worse with a lift and/or tall tires with flexible side walls. But XJ´s are most always better than YJ´s. A YJ will work on you a bit and rock you real good.
The top joint on the trac-bar? Trac bar play can often be heard, when someone is turning the steering wheel, a couple of inches left and right, and another has his ear, near the top trac bar joint. It clicks. Sometimes hard to see or feel. Doesn´t take much play to make the Jeep wander some.