Overprint fills don't quite get it

I have a file that was converted for me by someone using Illustrator.  It is a complex image.  There are areas where there is a black object behind the object I am working on. 

Here is the scenario: The object on the top is filled with red.  There is a black object behind the red object that is creating an outline effect.  I need to print on a red pen so I want to make the red object on my screen no fill so the pen color comes through.  However, the black object behind is preventing me from doing this.  I used to be able to use trim and it would cut out the black object so it wasn't there and the red object is able to be changed to no fill - this isn't working because the black object is ALL OVER the place creating outline effects.  I think what I need is overfill but not sure how to make it work.  If I print color separations, the black object is not printing, just the outline effects.  What I need to do is change all of the red objects to be no fill and let the pen color come through but trim isn't working.  Any suggestions. 

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