It's absolutely not impossible to fix. A ArtNJ has you on the right track, I promise. Ignore anyone else who has negative input about this including your vet, and focus only on a positive outcome. Your cats are sponges for your emotions, and how you feel can make a very big difference in how you approach this as well as in how they perceive their world.Some people are telling me this is impossible to fix and one will have to go
Also try some cat music - there's Spotify, youtube and Alexa, RelaxMyCat and MusicForCats as sources which can help mitigate any residual feline tension.
I apologize but I ran out of time and wasn't able to read every post so I don't know where this aspect stands. You mentioned earlier that you were wondering about removing the stray cat from outside?
Not only remove him/her permanently (s/he could be sitting in the next yard over and the wind could blow the scent right to your door), but do your best to remove all scents of that cat from your property. Lemon scented furniture polish can be used fairly effectively. Cut up some waste cloth, spray the pieces liberally and scatter them right in front of that door and also around the yard. These will need to be maintained/freshened.
I'm sending all sorts of positive thoughts and vibes!!