My cat's stool doesn't stink since we feed raw, so we don't have that problem.
Even if that was the case though, I still wouldn't use a self-cleaning litterbox. How are you supposed to know if there's something wrong with your cat? Often times the first (and sometimes only) symptom shows up in the stool or pee. Your cat could be having diahrrea or blood in its stool or pee for months before you realize there's a problem.
I've also heard that self-cleaning litterboxes are not very hygenic, but the above point alone is enough for me to stay away from them.
Maybe you should set up a system with your husband, where the first person to get home or the last person to leave for work has to be the one to clean the litterbox. OR have one person do it on even dates and the other person do it on odd dates, or something.