Hello and welcome. First, see the vet again, or a different vet and have a urine sent out for a culture
. This is a process that takes a little longer but is a more in depth analysis of the urine.
Secondly, you need to use an enzymatic cleaner on the door. Enzymatic means, it breaks down bacteria. And you have to really soak the door. More than once.
Or better yet, put in a new door.
When a cat avoids the litter box, there is always a reason. Either illness, or territorial or stress. It's the human's job to figure out the reason.
She clearly has had some stress, moving, and a change in routine, and stress can cause physical illness in cats.
It's quite possible that the door had been soiled before by other animals and your cat is objecting to that smell and covering it with her own. And/Or there is an animal outside upsetting her.
Spraying her with water won't teach her anything except to hide when she does it.
Install some feliway plug in diffusers to help with territorial issues and stress.
Clean the door daily with an enzymatic made for pet urine cleaner such as nok-out.
Get her urine sent out for a culture.
Reduce stress in the home.
Don't rule out medication as a possible solution. Amitriptyline is often used successfully in cases like this. But the health issue and territorial issue has to be dealt with first.
"finding her a new home" should not be an option. Who else is going to want a cat with litter box avoidance problems? She will end up abused or dumped on the street. I'm sure you don't want that for her. Pets are for life, when they have problems we deal with those problems.