Here is a link in this website talking about spot colors in an Illustrator drop shadow.
http://www.prepressforums.com/module...ewtopic&t=1368
I recreated the artwork based on your description. With regards to making a "Spot Drop Shadow" in Illustrator, there are several work arounds.
Take off the drop shadow in Illustrator, copy the logo, then open up InDesign and paste. Then create a spot color drop shadow in InDesign. That is what I tried and it works.
As for the already created InDesign file, have you tried ripping with Postscript Overprint set to "On" when you ripped?