You are not going to be able to do much.
The first problem you are seeing is that when you are converting all the trimmed surfaces are re-appearing. You can select the right options in the convert tool to prevent this but you'll have to delete all the history on the object, separate it, and work on converting each piece individually.
Then the next problem you will have is all the poly tessellation will be horrible and you'll have to fiddle more with the conversion tool options for each part.
Then you'll realize you have seams all over the mesh because none of the parts edge verts will be likely to match.
and finally after lots of wasted time you'll realize converting complex trimmed nurbs parts directly to polygon meshes is pretty much a complete wast of time.
I have had some success taking the nurbs model and making it live and then manually rebuilding a clean poly mesh on top.
You can also use tools like topogun and 3d-coat, to model over the top of the nurbs form a little more efficiently then in maya. But I still have not come up with an efficient workflow to do this in any package yet.
"If I have seen further it is by standing on the shoulders of giants." Sir Isaac Newton, 1675
Last edited by ctbram; 09-02-2013 at 07:33 PM.