I know this is really hard for you because I went through something very similar with Emily. I had reached the point where I actually thought about having her PTS. I wasn't willing to dump her outside and the shelters where I was living at the time were very high kill.

I spent lots of money on antibiotics and tests for her. The only thing we could come up with is that she is very sensitive to UTI's. I am still really careful when she starts to pee outside the box.

I did try a few things that seemed to help alot. This is going to sound crazy but a night-lite actually helped quite a bit. I am not sure why but it works (maybe I have a cat that is afraid of the dark...)

Another thing I found helpful was to have covered litter boxes. I don't have a door on the front, but they have a top to them. (not only do I have cats that are afraid of the dark, I also have cats that get embarassed easily )

It is a matter of trial and error to find out what will help...