Have you looked underneath while someone turns the wheel 1/4" each way? I never had a problem with play in my 2003's steering but the steering on my 2001 had a lot of play from day one due to side-to-side movement of the sector/pitman arm shaft. There is no adjustment for this and the two aftermarket gears I tried were the same way. This was before the aftermarket steering braces were available. I always thought one of them would have fixed it up because they place an additional bearing at the end of the shaft. I can't say for sure though because I got rid of the truck before the braces were available.
Regarding steering gear adjustment: If you are planning on winging it instead of going through the detailed off-the-truck procedure, it is awfully easy to over-tighten it, causing it to bind a little and not return to center. Not that I am against winging it; I am all for it. Just take good notes about the current position (mark it if you can) and be careful to keep track of and take notes on how many 1/4 (or 1/8 turns) you adjusted it from there. It will make it easier to go back to original if necessary.