Loose bearings in a hub should pack into the hub cup with about 2mm of space still left so they can spin freely.

It is not possible that the wheel was not properly seated in the dropouts/ends, otehrwise the whole rim would just rub on 1 side, not woble back and forth.

The only way this would happen is if the rim was out of true, but since replacing the bearings solved this without spoke ajustment is was something in the hub. The only other thing I can think of is that the cones were very loose, which would have been corrected with reassembly on the 2nd try.