We had an elderly cat (who recently passed) who did the same. After hundreds of dollars of tests etc...we found 2 things:
#1 - arthritis. The litter was not accessible enough for her to get too. It was located downstairs. We moved it upstairs and everything went well....for 1 year.
#2 - after the year - she went back to urinating everywhere. Again more tests which reveilled kidney failure (not sure why it was not originally diagnosed). This could not be cured and she died only 2 weeks later.
I say get a 2nd opinion. Had we done that in the first place, she still may be here.