Bending paper cutouts to match an existing logo

I have to match a design from our design studio for an animated intro to a website.

I created the paper cutouts from the logo, then put a curve modifier on it. The problem is that I just don’t have enough manipulation control to match the logo once I add the modifier (plus, dramatic changes to the curve or set up tweak out the objects and I have to start over from last save).

Here’s a link to a couple of attempts (the image I’m trying to match should be packed into the .blend).
Click Here for Files

Is there a better way to do this???
Thanks Blender Community!