At the interview she wasn't particularly nice and cute and the normal level of wary you'd expect. She was the stink eye kid, not doing as she was told and with parents laughing at her cuteness when she did such things.
That was your first clue - Although of course there are times we all take children we have some concerns about, I do insist on children coming to interview and I do monitor how that child behaves and how/if the parents react to it. So often, when I child doesn't consider their own parent's as being an authority figure, they also expect to come into my house and rule the roost and that's never going to happen.

In terms of this particular little one - I do feel for you. I've been really fortunate in only having this level of upset twice. Once with a little girl who is still here and it was a good three months. Sure, there were gradual improvements but golly it was slow. For her, she wanting picking up all the time which I won't do and it only really got better once she became more mobile herself. The other time, it was a little girl who had been cared for by family and she had horrible anxiety. In the end, I was saved having to term them as the Mom decided that grandma's was the best place with some professional help for her stress levels. Her hair would fall out in clumps and she'd just scream.

Of course, only you can determine how long you are able to deal with this. And I do understand, it's not all a mental health decision but a financial one too. I would be advertising with the hope of finding a replacement and if this child settles before then, great. At least it would feel like you are doing something productive to end the situation when everything else you are trying with this child, isn't quite working.

Someone mentioned elsewhere setting up a safe zone for cryers who struggle to adjust. A play pen or something, tucked a bit out of the way, where they can observe safely, where they will gradually calm down and which allows you to get on with your activities with the others in your care. Maybe this might help.

How old are the children you have? Do you have a local park or somewhere you can walk? Sometimes changing the scene entirely is a big help and walking gives them something to do. I have found getting mine outside (I have a large wagon thankfully) is a big help to most who are tearful in the house. Plus it helps wear them out so once they've had lunch, chances are they will sleep harder for at least a while. - It's only ever failed to work once for the girl with anxiety as she hated walking and would just sit on the ground and refuse to move! But for the most part, sure, you might have a couple of outings with screaming and tears but by the third day, they usually stop crying for the duration of the walk anyway.