Navy, I'm having a hard time understanding how a force can be generated to cause the whole rack to rotate against the bushings. Unless I'm wrong the rack & pinion are both simple straight or spiral cut spur gears which don't cause any torque load. The gear lash adjustment on the rack & pinion is only to deal with excess play in the wheel, as I read about it (at the very end of the link 36 sedan posted above).
The only thing that makes any sense to me is that maybe your steering arms are describing a vertical arc as they turn, imparting a "twist" on the rack? I'd try loosening the lock nuts on the threaded steering rods to allow them to rotate a bit as you turn and see if the housing movement disappears. If so you may need to tweak your steering arms for better alignment? Does that make sense to anyone else?