Poor baby
We have been very fortunately in that Ellie has never had a cough. It must be so frustrating for you. Hopefully the new vet will be able to figure it out.
Ellie's vet is very similar to yours. When we had liver issues going on and urination issues that wouldn't clear up and allergies starting, she was getting really frustrated because, despite her best effort, nothing was working. We almost had to go to a specialist but things started lookng better just in time. You could tell she just wanted to help so bad. It must be hard to be a vet. I really feel for people that can't find a vet that cares.