I am dumb! Just reread the post below and you already have thought of putting it on the dryer. Can your cat get up there?

I liked the idea - Catmandu's I think - of having a clear plastic/plexiglass house secured to the floor(with a liftable lid) with a kitty size door in it. You can maybe secure it with double sided tape or something - or if it is a big plastic box with hinged lid and a bottom on it, then you don't have to do that.