The Filling Station and Chevs of the 40s both have parts to fix your steering system. Looseness can be anywhere in the system. You mentioned the steering box. That might be the issue. However be sure to check the idler arm, the drag link and the tie rod ends. Any looseness anywhere in the system will cause your steering to feel loose.
In the steering box, I have found that the bronze pitman shaft bushings are frequently the problem. See if you can move the pitman arm shaft, that sticks out of the steering box, try moving it towards the front and rear. There should be no movement. Replace the bushings if there is.