So sorry for you dog:( I know how sad it is, i had to put down my 16 years old dog . She had kidneys failure. I was devastated but you know its just cycle of life . I thought that my dog and your dog had a good and happy life. We took another dog from the shelter. I decide that it time to rescue another life.
About fungal infection. Are you sure it is fungus? Fungus is white growth, may look like ling strands of fine hair or small patches, fuzzy. Can be gray,white or milky.
Also fish can have excessive slime coat due to infection , which you was treating him from. Also he might have bit of the slime coat from using salt.
Slime coat comes off the tips of the fins and sometimes the body. Slime coat usually slimy,clear like a mucus. It a natural fish protection against of the disease. Fish will act otherwise the same.
Be careful with all those medications , you don't want to over medicate him. And do not use API until you sure it really fungus. Do you still have him in the hospital tank? I don't remember how big it is. You already using medications so finish it and see how he doing and keep him in the super clean water. I don't remember if you using stress coat which is good idea. Stress coat and salt that you was using all together also can promote slime coat.
Is he acting healthy?