So, when the original shapes began to get lost as the kids attempted to paint every other space of a complicated design, I reminded them that it was just a sheet of paper, and that no matter how many mistakes they made, nobody would notice, because they would all still look great in the end. I was right, wasn't I? We solved the problem of the disappearing shapes by outlining them in black (painted with a giant Q-tip). We cleaned up messes by adding polka dots, and painted black and white frames (which the kids called "cow frames").
I think they turned out great in the end!