What about the condition of the steering box, steering shaft, length of shackles, condition of steering column, tire pressure, tire size, arch of leaf springs, and
caster? An alignment would probably help, along with a trac bar. When you said that you were moving back and forth, was the Jeep just swerving in the lane as if from over-correcting, or did it feel like the axle was moving side to side more so than the Jeep? Any vibes? I would get the front end up in the air, check for play EVERYWHERE, and plan on installing a trac bar and having the alignment done asap. Chances are a steering damper will help as well. What are the axles out of, and have they been rotated at all in a way that would affect the
caster? Poor caster would cause the Jeep to be squirly at higher speeds. Also it is just possible that you still need to adjust to the new handling characteristics of the Jeep (especially if it is lifted higher or has larger tires than before). On my CJ with 3.5" of lift and 32's, no trac bar and original steering damper, the steering wheel would be turning back and forth 90 degrees on the freeway at 70mph to correct for bumps. However, it was just slopy no matter how far I turned the wheel and would not suddenly be responsive. It was a compilation of several factors that affected this.