That put-a-rock-on-it idea is excellent. I've noticed in my garden when I use cardboard mulch (even 6-ply) and hold it in place with rocks or bricks, those spots are by far the very first to decompose. I suspect that it is the constant moisture or constant contact with the soil (or combo) that does it, as the rock doesn't allow it to dry out as easily, which is what seems to make dog poop last forever.
Excellent tip!
Sue