Seems like there are two veins of thought here - one is revolving
around how to get the smell out of the rug and the other related one
is how to improve his litterbox habits.

It's the second one that puzzles me. Jim, you did say he "sprayed"
right? Spraying is not the same thing as peeing, and cats do it for
totally different reasons - so I don't think that playing litterbox
games is going to do the trick. You've got a formerly outdoor cat,
who's now marking territory inside the house. Not only that, but he's
doing it in a manner that is designed to attract _your_ attention
(spraying right in front of you).

Question is why?

Getting the nasty rank smell out of the rug is going to help, but I
think that the problem solving ought to revolve more around why the
cat now needs to mark territory inside.

You say there are no new pets.

How about new members of the household? How long has Emily been
around? Is she pregnant (not being nosy - cats can smell these things
& sometimes flake out)?

Have you moved recently?

Have you moved the furniture recently, exposing a spot in the room
where a former tenants cat marked?

Have you brought any used furniture that might smell of other cats in
recently?


Have your brought in new furniture that was treated with
anti-flammables and is outgassing and creating smells that are
invisible to you, but not to him?

Have you or Emily changed your patterns of being home - started
spending more time away due to job or whatever, so that Rutherford
feels like he needs to call you back, or spending more time there so
that he feels infringed upon?

Is your relationship ok? Have you been fighting or engaging in
situations that cause tension in the household?

Have you had new friends start spending time in the house?

Something has changed - cats are flaky, but they're not insane, and
they don't do things at random. I'm not suggesting that you've been a
Bad Cat Dad or anything - just that sometimes cat psychology responds
in very different ways than people psychology. Rutherford sounds like
a well-adjusted cat, and judging from these pictures, loves you and
Emily - he's suddenly started spraying, ergo, something has changed.
Issue is to figure out what...

Hope this helps,

TG