A question about "facilities"?

I have had the same issue. I finally began vacuuming the floor very well before cleaning it. I use a Dyson Animal vacuum that is designed for cleaning areas where there are pets. It has a bare floor attachment, and I have found that it does a great job of picking up all of the fine particles before I clean. The thing suctions to the floor so tightly that it is sometimes difficult to pull it away. About once every two weeks, I use my steam cleaner to clean and suction up any fine powder that may be hidden. Try using a good cleaner that isn't prone to leaving residue when mopping. I use Armstrong floor cleaner, which has proven to leave no residue without rinsing. Also, if they don't already have rugs or something to trap litter as the cats exit the box, ask if they mind if you put one down. I have regular rugs designed to go around the bottom of the toilet under my litter boxes. These seem to trap a great deal of the litter and keep the residue down. I just take them outside and shake them each day, and wash them every 3-4 days.