How do I convert my Indesign documents to SVG files without losing/affecting my drop shadows?

I created documents in Indesign that have drop shadows applied to certain shapes.  I'm trying to convert these documents to SVG files.  Since there isn't a way to export from Indesign to SVG, I've been trying to utilize Illustrator.

When I select all and drag from my original Indesign document to Illustrator and then export as an SVG, I lose the drop shadow effect completely.  Instead of the shadow, I see a grey rectangle.

When I export the Indesign document as an EPS file, open it in Illustrator, and then export as an SVG, my shadows look like shadows, but they are broken up into pieces and have white spaces in between each piece.

I've tried other solutions such as releasing all clip masks and flattening the transparency, but nothing seems to be working. 

Is there a solution that will allow me to keep my original Indesign documents and convert to SVG without losing any elements such as these drop shadows?  Or will I need to opt for a more manual solution?  For example, replacing these drop shadows with a blurred rectangle instead?