Check for looseness elsewhere, rag joint, center link, idler arm, tie rods, ball joints, control arm bushings. Adjusting the steering box isn't a good move. If it needs adjustment, it's worn out.
I agree with most of this thread, the rest of the steering components need to be checked first, you'll need a helper to check some of it. After checking it, have your helper wiggle the steering wheel back and forth,just taking out the play to see if indeed the play is in the box, if so, you might be able to adjust it out.
Here is the method I use, jack up the front end and place on jack stands, loosen the outer nut on the allen head screw about three threads, you'll probably have to hold the inner allen head screw while doing this, next, turn the allen head screw in 1/4 of a turn, then move the steering wheel thru it's arc, lock to lock and see if you feel any tightness as you move thru the center position, if you do, you are finished, hold the inner allen head screw and tighten the outer locknut, if not, try another 1/4 turn and repeat the above method, good luck! DO NOT OVERTIGHTEN the steering box. if you don't feel safe to try this, find an old school front end shop and get them to check your car suspension and steering for you.