No advice, just wanted to compliment you and your wife on trying so hard to solve this. I don’t know that I would have the patience with such a hard situation.
Best of luck to you!
This. We haven’t had any problems with our cats so far, but they’ve lived <nearly> all 3 years of their lives in our same apartment. Not sure what’s going to happen when we move, but I might be back to this thread just in case. 
Go to a Health Food Store and buy a bottle of Bach’s Remedy. It’s a herbal blend that is supposed to calm every living creature. Kinda pricey, but many people swear by it.
You can Google it to learn about all the redeeming features.
~VOW
You can also google “homeopathy” to learn why it’s a complete scam.
I just discovered a pile of poop a few inches in front of the litter box. I think we may be finally getting somewhere!
My cats poo outside the box when (for example) anal glands are inflamed, urinary crystals are flaring up, the back end needs attention for one reason or another. It does seem behavioral, but have you popped the hood, so to speak, to make sure he’s not in some kind of pain back there?
For crimes against the carpet, Mr. Pooper is now doing hard time in the kitty penitentiary (one week in the downstairs bathroom). He’s got his auto feeder, fresh water, his favorite kitty bed, and, most importantly, his litter box. So far he’s been using the box for his number twos. He’s not a happy camper, by any means, but hopefully this will work.
I thought I would post an update. Mr. Pooper spent about a week in the slammer. After that, we decided to let him out during the day, but only after we saw evidence that he was doing his business in the proper place. Every morning last week we found a nice fresh poop sitting in his litter box (unburied, which was kind of weird), and so we let him out for the day. Three days ago we decided that it had been long enough that we ought to give him real freedom and keep him out at night. We left one litter box in the bathroom where he had been confined so as not to change too much on him.
The next morning I found two poops in the second litter box (outside the bathroom), one buried and one not. Clear evidence that Mr. Pooper had possibly been reformed, but I’d need to see that on a regular basis to be sure. No poops yesterday.
This morning I woke up to find a fresh pile of poop on the carpet, six inches in front of a litter box. :smack: So now I don’t know what to do, except keep him permanently locked in a bathroom every night (from where he’s managed over the last couple of weeks to partially destroy the adjoining carpet by attempting to claw his way out under the door).
Oh well, back to the drawing board…
Uhhh, that’s frustrating! 
FWIW, I started a thread about cats not covering their poopand learned/confirmed that it’s often a dominance issue. Possible that your kitteh isn’t happy with being in the slammer.
Tough beans, kitteh!
I can’t help with the rest since everyone already took all my suggestions 
but with the carpet clawing, you can put a chair mat down those ones that are used to allow an office chair to wheel freely on a carpet? Put it right up against the door or even close the door on part of it if it will fit. Usually that is too heavy for them to move so they just destroy something cheap and easy to replace.
It might be the carpet itself. We brought in an area rug that all three kitties thought was a perfect place to poo. Got rid of the rug, got rid of the problem.
Was the rug new when you moved in? Is it possible there were other animals doing the same thing prior to your moving in? Maybe have a professional cleaning with pet odor control stuff.
I swear by the ‘one litter box per cat plus 1, minimum’ rule. That would mean 3-4 boxes for you. Worth a try…
I was thinking about that myself - maybe this move was the final straw for stressy kitty and now he can’t share a box any more? Tho I don’t know how you’d be able to keep the other kitties from using “his”…
I’ve found that when there are extra boxes, each cat will usually pick one to use primarily, and will even defend it. I have 4 boxes right now (I have two cats ATM but leftover boxes from when there were more). Fairuza prefers to go in the one in the bedroom where she spends the most time, Caesar mostly goes in one of the ones in the living room, and the other two barely get used at all.
We now have four boxes and two cats, and yesterday I noticed my cat peeing in one box, then moving to another one to poop. If it keeps them happy, give them as many boxes as it takes. 
So. Any luck?