My Festie had a problem pooing outside the box after a bad case of worms. I think what caused the problem, ironically, was her preferring a clean house! She did not want to use a stinky litter box, and the combo of her and Gar pooing after worm treatments caused a major stinky litterbox.
I also think she had diarrhea (again related to being wormed), and the noise of pooing disturbed her. I did witness her run from the litter box on several occasions. What resulted, was she would try to hold in her poo, then ended up going on the bedroom floors.
I locked Fest in a cage for several days. If I was not home, watching her, she was crated. I put Gar in with her most of the time, as they didn't like being separated. The litterbox was on the floor of the cage. There were 2 shelves, and food and water were on the top shelf.
The problem was resolved very quickly in Festus; I don't know if it would be so quick with most cats. But anyone who thinks it is cruel to retrain a cat is crazy, in my opinion. Festus' problem stemmed from her desire for cleanliness (of the litterbox). I do not think she was happy to mess all over the bedroom floors. I think she was horrified, and tried not to poo at all, and could not overcome the problem. Once she relearned to use the litterbox, and I was extrememly careful to keep all litterboxes clean, she had no further problems.
I think every cat should be allowed a chance to fulfill their nature, which is cleanliness. I think it is cruel to get rid of an animal, or not to intervene if it is messing all over the house. If a short time in a cage returns your cat to its natural state of cleanliness, what harm is caused? (Short time varying from days to weeks.)
Until adopting Sugartoes, the cage stayed open and available to my cats, and they continued to enter it, as I kept their food in the cage (safely away from the dog.) It was never a source of punishment or cruelty, simply a way to teach my beloved Festie that it is ok to use the litterbox.
I have not read your original thread, but I have also heard of success with Cat Attract Litter. Good luck to you and your cat!