I successfully quit smoking (decades-long habit) a full year ago; I have recently begun experiencing dreadful tastes with every breath I draw. I can best describe these tastes as "wet ashtray". Mouthwashes of various types, extreme brushing of teeth/tongue/reachable areas of throat do not help, nor does eating strong-flavored foods.
My medical doctor has never heard of this and offers no suggestions. Any insight you can offer would be much appreciated.
Your experience of unpleasant taste and mouth sensations one-year after stopping smoking is unlikely to be a consequence of smoking cessation.
Improvements in taste and breath are in fact predictable benefits of stopping smoking that are noticeable within a week or two of stopping smoking.
It would be best to consult your dentist or an EENT (eye,ear,nose,throat) physician regarding these symptoms.