I had a similar problem but with peeing, despite three litter boxes and regular cleaning. He'd go in the same room, five feet away. It go so bad that the carpet started developing some sort of fungal growth, which was gross. I read up on it and apparently some cats develop a "texture preference," especially for carpet.

So in the utility room I used for the litter boxes, I replaced the carpet with some cheap engineered wood flooring (Pergo or some similar knockoff brand). Problem went away. I think it is very weird/uncomfortable for them to go on a smooth hard surface, and carpet is a rougher surface that sort of could feel like dirt or grass.