I have come up with an idea that might be a fix for the precision issue-- at
least for some of your lathe objects. I have not tested it thoroughly though; I
used only frame 3 of your animation for my test, the 'cubic lathe 1' object.

That shape uses your (first) array[6] for its construction points...

array[6]
  { <-3, 1>, <0, 2>, <3, 4.5>, <3, 9.5>, <0, 12>, <-3, 9.5>,
  }

....so I made an 'intersection' of the resulting lathe object with a box:

....
#case (CUBIC)
  intersection{
  box{-6,<6,12,6>} // same y-height as in array
    lathe { cubic_spline List (uv_Ctrls)  rotate 0 }}  #break
....

Even with Offset = 0, it looks like the trace at the top was successful. Perhaps
the coincident or overlapping y=12 values have somehow removed the tiny
precision error. HOW, I don't know.  ;-)

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