Some pet lover I listened to on the radio (NYC area - Saturday morning talk radio) said to put some of the cat's food on a plate where it left its mark. Repeat indefinately if they find new locations to make their mess. The cat (if it follows this guys logic) will move spots, and you basically repeat puting food out wherever they go until they make the brilliant connection that they should not leave their mess where they eat.
I can not speak from experience however, since my wife and I are not cat lovers by any means.
Regarding cat stains, I had three rooms with cat damage. The room with the worse damage didn't finish as nice as the other two with less (yet signficant) damage, but the others did come out nicely. I was on a budget (now paying the big mortgage) and was fairly pleased with the result. You might want to post a picture of the amount of damage your cat has already contributed to see if one of the very knowledgeable pro posters here can estimate the extent of your damage.
Regarding the enzyme cleaners (like nature's miracle), supposedly they take weeks to work, and they do eleminate the smell sufficiently. You may also be able to rent an ozone cleaner machine at a janitorial supply store if you want better odor elimination. But I would not expect the stuff to be a deterrant for the cat. I guess it acts as a odor eliminator for your guests instead.
Good luck.