Great advice from other members
I do not clean it as often as I should sometimes, but such is parenting.
Wish you had written that in your intro paragraph in post 1.
In my experience, by far
the number one reason cats soil outside the box is because the box is dirty. Simple as that. A cat's nose is much stronger than yours so if you can smell that strong urine/fecal litter smell - you can bet your cat smelled it days ago and is not thrilled about doing its business in a stinky box. When I was a kid and went to my grandparents' house and they used the bathroom to do their business....If I then needed to do MY business I'd hold it in or use another bathroom. Cats have less control than we do and can easily find cleaner spots to do their business. Usually humans don't appreciate the cleaner spots that a cat may choose.
So my rule of thumb is that the solids need to be removed every single day. And the litter needs to be completely changed every 6-7 days.
Given that it's the number one problem for soiling outside the box, this needs to be corrected before even thinking about other possibilities for this behaviour. Imo you are wasting your time considering other solutions if you do first address this issue.
Hope that may help - and good luck!