It may be totally unrelated, but in my old S-10 the pitman arm and idler arm were both old and worn out, turned out there was some flex going on when I would turn the wheel. I could be going straight and hit a slight bump and my truck would jump in a different direction. There's a small chance it could be your steering components, but it sounds like it's just your bigger, grippier new tires
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I am here:
http://maps.google.com/maps?ll=28.392185,-80.778937