Removing slop in manual steering

I would turn the shaft by hand under the hood also. There may be play in the box coupling. Just a small amount of lost motion there will equal what seems like a mile with the large diameter stock steering wheel.
If the input shaft moves in and out of the upper seal more than 1/16th changing the preload on those bearings may not help much.

You are right on with the input shaft moving in and out. My steering box had play with input shaft motion was so bad there was no fix. I found a good box to replace and it drove like a new car.