Just to be sure, the shaft is the internal shaft that is inside the tube. When you say upward movement is visible, do you mean the steering wheel moves up? The shaft with the threaded nut moves up? Does the bell move? Does the horn plate move up? Do you have the horn button off to watch shaft. Is steering wheel off? The 55.2 column is the
same construction as the 58, albeit different length columns. Aren't your Assembly Manual and Maintenance Manual for 55-59? I have a Maintenance manual for 55-59.
The shaft has a worm gear on the end, inside the box. It drives a "ball nut" which drives a sector gear attached to the pitman shaft. There are two adjustments. Lash on the side and end play on the lower end. There is a bearing on the lower end and one on the upper end (of box). If the end play is loose or the upper or lower bearing is screwed up, the worm gear will move itself and the shaft up and down, instead of driving the pitman arm. The worm gear needs to be captivated between the two bearings. I have a clear picture in my book and I have the adjustment procedure if you need it.
The end play (big lock nutted screw on lower end) is done before lash. Lash is just the pitman shaft. Lash is "backlash". Lash will have nothing to do with your problem. Be sure you have the correct procedure for what to disconnect before adjustments. For end play/preload: It says unlock nut, to turn the big slotted adjusting screw "until all end play is removed". Then tighten lock nut.
I have the steering wheel/horn/mast bearing assembly picture also, with parts description. I agree, I don't see how any mis assembly or problem up there could cause this.
I remember taking one apart. I think I took the side plate off and watched how it worked and check the upper and lower bearing retention. I would be careful not to release the balls that are under the ball nut. Instead of the worm gear meshing directly with the sector gear, the balls do the meshing. The famous recirculating ball steering.

Today called a ballscrew. Also similar to a linear bearing. These are used on precision CNC machines to translate.