Stressed cats often toilet inappropriately. You are right in that the litter tray has to be as inviting as possible. It does need to be kept very clean, but also situated in a "comfortable" place, away from disturbance, or any other cats. (If there are other cats outside which hassle yours, the litter tray might be better kept away from access points to the outside, such as near your back door. She maybe reluctant to use it near to where other cats go.) Also keep it away from where she is fed.
Fortunately if the above does not sort things out then there are a couple of other things which should help. There is a non-prescription remedy called Zylkene which can calm down stressed cats remarkably well. It is actually a food supplement, made from a certain milk protein, which acts on a particular part of the brain to cause a relaxed feeling. (It seems to mimic the contentment a baby kitten feels when suckling from its mother.) Zylkene comes in capsules which can be opened and sprinkled onto food. They taste very acceptable to cats, and one capsule a day (two for a large cat) for a while should help your cat a lot. Add it to a small amount of moist food.
The other thing which helps stressed cats is Feliway. This comes in the form of a room diffuser which releases tiny amounts of a synthetic pheromone into the air. We cannot smell it and are completely unaware it is present. However the pheromone does have an odour to cats and it stimulates another part of their brain to create a feeling of relaxed well-being. Keeping a Feliway diffuser in the main room of the house where she spends most of her time (probably where the sofa is) should help considerably.
Using Zylkene for a few weeks might help her to settle down in this new environment. A feliway diffuser lasts about a month, and you can get refills if you need to keep using it after that. Some people keep one going all the time if their cat tends to get stressed easily.
You can find Zylkene here and Feliway here on the website, or ring us if you have any problems.