If you are getting an acceptable result for a portion of it, you could still use the live trace. After the trace, you could expand the object for further editing (Object/Expand).
I also ran the trace with the Color 6 preset, and it looked pretty good. That trace had the sort-of transparent portions, as well.
As far as drawing or modifying the trace, you would use the pen tool to add or remove points and paths. Than, you could use the direct selection tool or the convert anchor tool to move points, or create bezier curves or hard angles.
Anytime you do an illustration, it's an interpretation of what you see. Maybe you want a slightly abstracted form.?
I'm not sure what your proficiency is with illustrator, so I'm being cautious with my explanation.