OP evidently refuses to try a brand new box so instead is going in circles...I agree, but some of those rack/pinion steering systems are 20+ years old themselves. Hardly "modern" IMO. Still, better than the stock G-body styles.
However, I still believe that the steering issue in this thread can be overcome. It shouldn't be wandering all over the road, even if it is the old circulating ball type.
I'm wondering if there's some internal seal leakage allowing pressurized fluid to try to go to both sides of the piston and bleeding off some of what should be the high side during a turn? I know I'm digging outside the hole here, but from all the responses here I'm starting to think there's something wrong with the box hydraulics, even so much as the pump, or something's worn internally.
I do agree that rebuilt units are a crap shoot. They clean and reseal the outside of the units at least, but they hardly ever replace the hard parts. Which is usually why they're being traded for new ones in the first place. I know you've already swapped your unit for another one, but I just wonder if you're getting junk boxes or...???