This is an extremely difficult situation. You won’t get a perfect result with a simulation. This is what I would do:
Modelling the paper won’t be a problem (make one, Displace Modifier, Global Coordinates, duplicate, Object > Transform > Randomize Transform).
Set the ground plane and ‘restrictor’ to passive Rigid Bodies (set ‘hollow cube’ to Mesh!). (Not to Collision!)
Set the paper to Active Rigid Bodies:

Play with the settings (use Mesh!) and copy setttings to all the paper:

Play the simulation untill you are more or less happy with the result:

Might still need to manually move a few pieces…
You will need to Bake to Keyframes, I think; to be able to move the paper.