Hello hope this isn't too late for you, and hello mograph community, its my first post.
I'm doing research in faking stop motion using 3D computer packages at the moment, and a few tips if you really want to add some depth to your animation. Firstly you have to remember that stop motion is animated using a technique used straight ahead, whereas keyframed animation that is done using computers or even cel used this method is known as pose to pose, as in you start with one extreme end with the next extreme and do all the frames inbetween, hence the term tweening. So what I'd recomend, is using the straight ahead technique in your animation package, move the character or piece of paper a bit, insert a keyframe, move on to the next frame, and do again until you have your end point. Won't look tidy, but thats the beauty of stop motion.
The next tip i'd give to make it authentic, remember that when the aniamtor moves the rig or character that he/she actually interacts with the object, and therefore makes some unitentional marks on the object, for example claymation, you can always see the animators finger prints all over it moving everytime they move the character, obviously animations like wallace and gromit, the animators are skilled and take care not to do this, but exceptional stop aniamtors like bruce bickford loves the textures the fingers add, and an important animator norman mclaren believed that with stop motion its the actual interaction with the model between camera shots that gives the animation its escence.
I also recently discovered that people can not really distinguish the difference between 24 fps and 8 fps and I myself always got better results from rendering the animation at 4 fps, to really give it that dirty stop motion effect.
Hope this was helpfull and not too late