if you have a perfect working rig it should run fine without a steering stabilizer. steering stabilizers cover up/dampen the underling issues. I would jack the front axle off the ground start with the drag link, and tie rod. shake all of them back and forth, up and down. look for any play in the tie rod ends. if you cant find anything move on to ball joints, wheel bearings, and u joints. check ball joints and wheel bearings by trying to move the tire back and forth and up and down. look for any play and when you find whats causing it replace it.
normally ball joints or wheel bearings will cause the whole tire to wobble and you would feel vibrations in the whole jeep and not just the steering wheel. so spend more time looking into all the tie rod ends first. :twocents: