I have 10 cats (all rescues and FIXED) and they all live inside which means we have several cat boxes. I use "Sweet PDZ" that I buy at the feed store mixed in with the clay litter to get rid of the smell. It is used in horse stalls to eliminate ammonia and it really works like magic. We can go a week between totally changing out the boxes where we used to have to do it every three days.
I do not know if it would dissolve well enough to go into the washer, but you could soak it.
I think, that there have been many other suggestions for getting the odor out of the fabric. I posted about Sweet PDZ for anyone who has multiple cats and deals with cart box odor.