I was just wondering if there's something in the environment outside the home that is bothering the cats - for example, stray cats coming in close to the house and interfering in their so called territory. This can set up all kinds of issues from territorial marking to fighting between the cat residents in the house. From the human's point of view, situations like this are missed. All we know is we have an issue and we don't know what started it. The poo on the floor at the basement door could be a territorial marking thing, as well as stress, as you've mentioned earlier.
Have you considered using an animal communicator to see if they could shed some light on your problem. I know there has been some mention of animal communicators when it comes to lost animals on this site. I think there's been some success in their use, I'm not sure maybe somebody else could shed some light on this subject.
Here are some websites that I got out of the Animal Wellness Magazine, maybe they might give you some ideas. Hopefully we can bring this to a happy and successful conclusion.