The sport edition should have the dark (almost black) wood trim and would have KDSS. Pretty rare find.
That said, if I had to do it over again, I would have gotten a 4Runner or Sequoia. I'd prefer to not have the air suspension, integrated Nav/HVAC, and the rear hatch of the 4Runner is infinitely better than the swingout door of the GX, IMO. Although some loaded V8 4Runner Limiteds are pretty close except for the swingout door. Integrating an aux or IPod is a hassle and you really can't upgrade the stereo if you are so inclined.
On the upside for the GX, the 2005+ V8 is very quick, there is a little extra room, they are probably more likely to have been well maintained/pampered (you can check at My Lexus), and I think they may actually be a bit cheaper than a similar 4Runner.
But if your time frame for searching is long enough, I would get the car you want. I can't speak for your particular area, but 4Runners/GXs are pretty much a dime a dozen out here. I would also recommend taking a look at the 2005+ Sequoia. If you don't find them too big, I think they ride as nice or better than my GX and both are more capable than anything I will ever need.
Issues with the GX are air suspension issues, cracked dashes (mostly early ones and in hot climates), and the typical 4.7L drivetrain issues. It is a pretty stout engine but the cooling system seems to have issues with radiators and the air injection system flakes out, but there is a cheap work around.
