No no, it's not that the litter box is too small or that the litter granules bother him. He's just too furry.
The main reason cats avoid litter boxes is that the litter box is dirty. Many cats won't use a litter box with feces in it, hence it's recommended that you have as many litter boxes as you have cats, plus one.
Since Amber doesn't work, she could have only one litter box. AS LONG AS SHE CLEANED IT AFTER EACH USE.
If she can’t walk for 30 min, she’s not having sex for any length of time.
If one only lies back and spread one's legs, and that is all the interaction had during sex, there is no exertion taking place.
I'm not saying she isn't a lesbian, but I don't think she gets pleasure from sex.
If the kitty has any of the above issues, or worse yet, a UTI, it hurts them to climb in the box and squat low, or dirty litter irritates their sore bottoms,
Cats don't sit on the litter, they hover above it. A non-treated UTI will kill a cat, and the symptoms are obvious enough that even Amber would notice - lack of appetite, pain, loss of weight and - eventually, if not treated - death.
A cat with an UTI won't use the litter box because it associate the box with the pain it feels when it urinates, not because it hurts to climb in the box or squat.
A blocked gland will make itself clear in due time because it will eventually burst open. Amber is negligent with her animals, but both cats parade in front of her (and the camera - so at eye level) a lot. She would have seen something like that, or a dingleberry.
Wasabi, and probably Rarity, has been defecating outside the box for a long time. Too long for it to have been any of the things you suggested. A dirty litter box, OTOH, was seen on at least one video (so dirty that there were pieces of feces falling off of it).
It wouldn't surprise me if Amber, instead of tossing away the clumps of urine and the feces, is dumping fresh litter on top of used until the box is full. It would explain her statement that she just throws away "old" boxes and buys a new one.
I bet the cats are also using the clean clothes she keeps on the floor (and her blankets, pillows, boxes and whatever other soft surface they find) as alternatives to the litter box. In short, they're peeing and pooping everywhere. After she gets rid of Rarity because of her "allergy", she'll become allergic to Wasabi.