They went to "T" style in 2008
That is incorrect. They went to the T style steering with the 2nd generation trucks. I know because my 98 came with it. For some reason, Dodge later went back to the Y style in the 3rd gen trucks. A T style steering is not a 3rd generation steering upgrade. It is just a late, 2nd gen upgrade. The only 3rd gen upgrade is the track bar. As stated several times above, requires an aftermarket bracket, which is NOT available through Dodge. Spicer or Moog Parts are built better than some cheap discount parts and should last longer.
Maybe that kit isn't such a good ideal. Does anyone have any suggestions on the wondering steering?.
Speedracer, many suggestions have been made.
As stated above: 3rd gen track bar/bracket, T style steering (just order parts for a later year 2nd gen), steering box stabilizer, Borgenson box and steering shaft, ball joints (if nessesary), Caster.
I would probably check your control arms and hub bearings while your at it. Sway bar ends won't directly effect wander unless you have a top heavy load, but I would check them as well. There probably isn't one answer. More than likely, it will be a combonation of the above. If every part is worn a little, you will be all over the road. If ball joints are tight, I would start with the track bar, t style steering, and a good alignment and see where you are at. By good alignment, I mean an "alignment shop", not Tire Kingdome. Maybe someone will chime in with alignment numbers that worked for them.
It is unlikely the ball joints are sticking. If you believe they are dry, I have added grease by using a grease needle and injecting it into the rubber. I would not do this if the rubber is good and holding grease.