Mask/clip shadow

Hey guys,

I'm about to go crazy as there's seemingly no way to achieve what I'm trying to do. I'm working on a logo that involves a card – like an index card (see below – it gives you an idea how I built it). I've positioned two slightly curved objects underneath that card and gave them a shadow so that when my rectangular card is filled, it looks as if the card is slightly bend on both sides.

This works fine, as long as the index card is filled – however, I wanna give my client the option to position the logo on a e.g. photo and I want only the cropped shadows and whatever is on the card to appear – the card needs to be transparent. This works on plain white background obviously (when it's filled), but not on a photo or pattern or colored background.

Is there any way to achieve this in Illustrator? It would be a piece of cake in PS – I'd rasterize the layer effect and and then just crop it with my index card shape and I'd be done. I'm asking because I'll need SVG and AI files too so PS is out of question.

Many thanks.