Hsv-1 in mouth and likely esophagus has therefore invaded the vagus and glossopharyngeal nerves causing dysautonomia. can hsv-1-killed nerves recover?

Complex, unusual: HSV can cause nerve-related symptoms, but usually doesn't destroy nerves, so I would expect recovery. However, this is an unusual and complex problem. Such extesnive HSV1 infections can occur in healthy persons, but mostly in the presence of immune deficiencies, especailly cancer chemotherapy, radiation, etc. You need specialty care, e.g. infectious diseases, neurology, and/or otolaryngology.