I remember doing this as a child on our TV that had a picture-in-picture setting. I would set the same channel twice and cross my eyes pretending that it was 3d TV.
How does that work when the two images are different sizes and overlapping? Did your PiP mode have a split screen option? The ones I've seen only allowed moving where the insert was placed (which corner), but it was always a PiP and never a split screen.