Would the information at this link be of interest to you? It's a write up by ENT Jamie Koufman on neurogenic coughs. She talks about its symptoms, and treatment, which she advises a combo of gabapentin and amitriptyline. She outlines the doses and time frame (i.e., not forever). She also discusses the role of the vagus nerve in coughing and digestion .
https://jamiekoufman.com/what-is-a-neurogenic-cough/