Based on that inspirational video, what you are setting out to do is much more involved than just a bunch of PiP's (though those sheets will basically be PiP's, just lots and lots of them). I also noticed that the exact orientation of the "sheets" varies a bit. It adds a dynamic, edgy element to the video, so you might want to think about doing an alignment grid in Photoshop (providing that you have access to it), where you create several non-Filled Shapes (thin Stroke only), in the dimensions of the sheets, on separate Layers, and apply a bit of Rotation to them. I would do those in different colors, and jot down the colors based on their degree of Rotation, so that you would know that say red rectangle is 5 degrees CCW, etc.
Looks like a very interesting Project.
Someone above mentioned After Effects, and I would tend to agree, if you have access to it. There might even be an Expression available to "automate" things a bit for you.
Good luck,
Hunt