I would say stick with UC Davis. None of the things you mentioned will hurt him but not going to heal whatever the root cause is.
For the cough, I would just keep him calm and cool ... obviously he does have CT because it was visualized on xray. Of course, there is no way to know the severity of it without a flouroscopy as Taylor mentioned.
I have found that CT dogs each respond to different protocols. Have you tried lomotil? I have a foster who is on it for CT and it is helping him. Many of the specialists are now using it.
Here is a good link to read....I would pay particular attention to medical management of CT:
https://smallanimal.vethospital.ufl....heal-collapse/