Well can you see any imperfections in the ball itself? Nicks, scratches, dents, etc. If not, then I would tend to say the problem isn't the ball itself.
You say your CP tilts to the left by about 1/16". That may not sound like much, but when you remove that inertial force holding the TB still and get it to spinning then it has the potential to go any which way. Is it a 3" trackball? The heavier the ball, the more likely it is to be affected by the tilt.