It's good that you've attempted to rule out any physical disability, which might be affecting her. However, it could be worth another visit, just to be on the safe side if you're thinking it may be physical rather than pschological.
Or, possibly, as she's part rag doll, and presumably quite fluffy, she may find the type of litter is causing static and giving her electric shocks. It can apparently be problematic for longer haired cats, who can generate and pick up static more easily. (just a thought!)
Also, cats dont always like to have their litter boxes tucked away in private places. They like to see whether or not they're going to be ambushed during a very vulnerable moment, which is why although boxes with lids are favoured by humans for their cats, a lot of cats dont feel particularly safe using them.
Jackson Galaxy has some very useful information on his website, and I found this link, which could help to give you valuable clues as to your girl's behaviour.
You could also consider "sight screens" on any windows where the outside cats may be able to see in - that could be an opaque material stuck to the glass, or cardboard taped over it, so it prevents her seeing other cats and from them seeing her.
http://jacksongalaxy.com/2014/08/18/cat-mojo-why-does-my-cat-pee-outside-the-litter-box/?utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+JacksonGalaxy+%28Jackson+Galaxy%29Is it possible to her to have outdoor access without having to leave the garden - ie could you cat proof the garden and then give her access (maybe not possible if you're in a flat or dont have access to garden space)?
The blacklight torch Kay suggested is a good idea, as you could then check outside and see where the visitor cats may be marking and see if there's a correlation to where your cat is weeing.
What deterrents have you tried in terms of the outside cats?