68 Barracuda Manual Steering Box

if you have pending return with PST cool, they should be able to make a decsion on if there is a fault with the steering box.

If the box is assembled with care and good parts, any movement of the input shaft should result in a movement of the sector.

if you can turn the input shaft with no movement of the sector then one of these issues is the cause

1) Sector shaft teeth are not meshed with ballnut teeth to the appropriate specification in the middle of the box travel (straight ahead). The teeth on each of theses components are wedge shaped in profile when looked at, from the side and when looking face in. The sector tooth is wider at the top and sticks out further at the top than at the bottom and the bullnut tooth is the oposite
The bolt and locknut on the cover of the box dictate how hard the sector shaft teeth are wedged down into the ballnut teeth, bolt and locknut dicate how hard you wege those opposing tooth shapes together.
Any space between the two results in sloppyness. But too much "wedge" leads to wear and a very very stiff section in the middle of the box.
If the upper mid and lower sector bushes or bearings are worn out the sector is not well supported so you can not depend on the mesh between its teeth and the ballnut.

2) The ballnut, worm screw and the ball bearings used between them, have a tollerance stack up, in the worst-case direction. thread in ballnut too big/loose, thread on worm screw too small/loose, or the ball bearings that sit in the threads between the two parts are too small. given that we are pretty good at making ball bearings spehrical, and, to size i'd assume something with the nut or the worm. you might get away with hardchroming the parts to make them just a bit bigger or trying a bag of different size balls, you need about 60 and hardened makes sense.

3) the area you highlight in the picture. The hex ring is a big lock nut. its is tightend round a thread cut into the screw-in aluminium end to the steering box. On assembly and before the sector is installed the is section should be screwed in to give a precise level of preload to the worm shaft bearings, measured as a turning resistance, and the lock ring is applied to keep this set. The worm shaft rides on caged ball bearings much like those used on the peddle crank of a raleigh or schwinn bike. If this has not been done properly or the bearings are broken, turning the input shaft allows it to rise or sink a tiny amount in the case before it starts to move the ballnut, hence when magnified at the edge of a massive mopar steering wheel you see this as play

any one of these things could be casusing your issue , and all are hard to spot with the steering box in the car.

other things cause the same symptoms.
busted steering box mounting on K frame or chassis depending on age, or which side the driver sits.
loose column causing worn or damage to the pot coupler or rag joint
worn out pitman arm track rod ends etc

A nicely rebuilt or brand new steering box should be stiff in the middle. This is by design and stops the teeth chattering and wearing between ballnut and sector when you drive straight ahead, you will find it hard to turn the input spline with your hand, without it being uncomfortable and the smallest movement you achieve should create an instant movement of the sector.
if you can twist the input spline and get no sector movement the box is potentially at fault.

If all adjusted correctly, and you still have the problem, its a problem with the parts used to build the box, not the setup.

I've built a few of these over the years and have found a range of horrors, but all were rebuilt to fight another day with no slop.

Dave