There was only one outlet hole by the taps and the washing machine outflow was fixed in it. Fortunately, I have another drain in the utility room, in the floor, for opening up the water heater and for the condensate from the indoor part of the heat pump. I took the hook off the end of the CatGenie outflow hose and just stuck the hose down into it.
I finished putting it together, and ran it. I knew it ran a long time -- 15 minutes -- but at least it's much quieter than the Litter Robot. I brought a chair to the door of the utility room and watched. It probably would have helped if I'd watched the video on the CatGenie site because I was sitting there thinking "Oh, *that's* why it's doing that." Both Shiva and Giorgio came and looked into the utility room and then walked in on alert. Spirit stayed in the cat castle for most of the time, and then ventured to the end of the hall. As soon as I was out of the way, Shiva went in and used the regular litter box. CatGenie says not to clean it to encourage them to use the new one, so I'll be watching.