I was always told there should be a minimum of one litterbox per cat, because some don't like sharing.
I've had luck with moving a box (more than inches per day) by doing it immediately after cleaning the box. They always seem to want to mark the box after a cleaning, so they are waiting to mark and paying attention to where I put it. If they don't see, I will pick them up and and talk sweetly as I put them in it. You don't want them to in any way think they are being punished by putting them in it.
That being said, I would like to know, isn't pooping supposed to be more of a stress reaction? I remember being told that when a cat started acting up after a divorce. So did my kids.