It sounds to me like the rebuilder may not have done the setup on the steering box correctly. There's two parts to it on a stock steering box, worm gear bearing preload and sector engagement. Those can be adjusted on the truck using the instructions in the service manual.
Another possibility is the balls on the steering arms being worn out, but you said you rebuilt all the components.
You can check where the play is by observing each component as you move the wheel back and forth. Methodically check everything all the way to the front wheel bearings.

You'll find the issue once you do that.


Kevin
1951 Chevy 3100 work truck
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1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car)
Busting rust since the mid-60's
If you're smart enough to take it apart, you darn well better be smart enough to put it back together.