my bad.
i was under the impression that the spindle was the part that was still loose, but your axle ends are where you're getting too much play. i have heard that you can bore out the axle ends and install larger diameter pins to compensate but i have not done this with my truck. i just replace king pins and bushings in the spindles.
atomarc- as far as the bushing that are supplied with the new king pin sets, the do fit over the pins most of the time, but after they are installed in the spindles they are supposed to be reamed to make sure there is a straight line from the top of the pin to the bottom to avoid binding when the steering wheel is turned.