Hi Mary,
Are you swapping the cats themselves? I know they are re-discovering themselves via the basket but I wonder if you actually swapped areas for the cats they may feel (or rather Sox) less determined to claim a certain area of her own (especially if in that area is also her food and tray).
Spookily I have just finished reading a book (Jackson Galaxy - Cat Daddy - its really good) and it explained this behaviour quite well, about a cat who attacked everyone from sitting on the landing outside the bedroom door (even resorted to drawing blood landing on their heads) but was fine with its owners & their children. Anyway they looked at what was in upstairs that was suddenly make the cat feel so in need to protect it and viciously too and anyway, they found that not far from the kids room was where they had the tray, food, toys for the cat. They removed it all. Spread out the toys, but the tray downstairs and the food in another room and the cat instantly changed.
He said the cat felt like its territory was just that small space upstairs and because everything it had was in there. Because of this the cat defended it with its life - but when everything was spread out it saw its territory as the whole house, it then instantly relaxed because the territory was large enough for itself, his family and any visitors to come and go - so the cat didnt feel the need to defend as he could safely watch people in his territory without them giving him the feeling they were "overtaking" it.
I'm not saying this is the problem or that Soks will be a darling (we could hope) but maybe the removal for a short time of Moet (may into a bedroom) and just expand Soks world, put things back how they were and no longer shutting the door, might help her relax and then bring Moet back??
Its worth a try? perhaps??
Whatever, happens - good luck with the vets tomorrow x