After months of trying to keep Kana off the couch, I give up. She has won. She has two points in her favor that were a big part of my relenting: she was allowed to sleep on the (different) sofa in my old house, and because she can't go outside by herself here - like she could at the house - it's the place in the apartment where she can find a sunspot (a vital ingredient in her life).
I was attempting to keep her hairy and often muddy little dog body from dirtying the beige futon cover, but alas alack, I can no longer. Besides, letting her sleep on the sofa often lets me sleep longer in the morning. I guess we both win.