Hi there,
If there is still a suggestion of reverse sneeze, or if the cough sounds moist, then adding San Ren Tang and using it together with SMS may help with the cough. Coughing occurs when normal Lung Qi descent is obstructed, with Dampness and Phlegm being a major cause of that obstruction. San Ren Tang helps reorder Qi descent and drain Damp that is in the way. Si Miao San, while anti-Damp, doesn't really do much for the airways, so you may need the two together to achieve a more comprehensive improvement.
Wei Ling Tang has been helpful in my hands when dealing with a wet cough, and would help reduce the Spleen deficiency causing Dampness and the craving of garbage, yet is warming. If the dog is heat intolerant or anything, I wouldn't use it.
Also, for a Cushing's dog that is somewhat improved on Si Miao San, it suggests that if the owner moves to any sort of fresh food diet (whether raw, home cooked, or commercially cooked and refrigerated), the improvements should be wholesale and pretty rapid. To comprehensively and meaningfully improve the dog, such a move is necessary when you see a clear response to SMS. So I would do that as well.
If you're still struggling after that, then maybe you're dealing with a sequela of Damp, like Shao Yang disharmony. Normally it's more of a consequence of Blood or Yin deficiency, but can occur with Damp, causing Stomach dryness and Heat, as well as Qi stagnation issues in the Triple Burner manifesting as a cough. Minor Bupleurum might help with that if it's present, but I'd use SRT and diet change first.
Lastly, Yin deficiency can occur with prolonged Damp Heat or with Shao Yang disharmony, producing profound dryness. If the cough is dry and harsh, without a hint of moisture or expectoration, then a moisturizing formula for the Lungs may assist. If you try XCHT and it helps, but not enough, then Yi Guan Jian is the next step after that. If Minor Bupleurum isn't helpful, consider Bu Fei Tang. Since these are moistening formulas, you'd need to be sure of yourself before using them in a primarily Damp animal, so I'd implement San Ren Tang and diet change first.
Hopefully this helps you out!
Steve