Are you checking on-center, or off to the side? There is deliberately some clearance built into the worm off to the side.
Also check for any looseness in the column, and where the worm is installed on the column. I seem to have problems with the steering wheel getting loose (although not that loose).
Otherwise, it comes down to proper, careful adjustment of the steering box. Whatever you do, DON'T just reef down on the adjusting screw trying to take out the play! I've tried that route several times, and the results have not been pretty.
You need to at least have the Pitman arm (aka drop arm) disconnected from the center link. IMO it's better to have the box out of the car, but it can be done in the car. First step is to back off the adjustment screw (or just remove the top cover) and measure the worm end float. Although in theory you should be able to just take out all the shims, install the cover with the bolts finger tight and measure the gap; I have not had very good luck with that method either. What works best for me is to assemble the box with an extra shim, then use a dial indicator to measure the actual resulting end float. Then remove shims to equal that amount or slightly more. As the books says, a slight amount of pre-load is acceptable, but there must be NO end float.
Only after you make sure the shims are right, you can check the adjusting screw. With it properly adjusted, you should be able to just barely feel a tight spot near the center of travel. It's a lot easier to feel with your fingers turning the shaft directly, rather than with the wheel.
FWIW, my most recent go-round with the box on TS13571L turned out to be that the new peg was working back and forth in the arm. You might want to check to be sure the peg is solid with no movement whatsoever. I just replaced the arm rather than try to deal with the waddled-out hole.