Hyperthyroidism causes some cats to have a hoarse meow but it usually causes weight loss even though the appetite is the same or increased. If you start to see signs of weight loss over time it would be a good idea to consider this possibility. Laryngeal paralysis can occur in cats. This is a condition in which the folds of the larynx which should pull back to allow the larynx to open during breathing do not do so. This condition is diagnosed by visualization of the larynx under anesthesia, so it is best to check for this while checking for polyps and cancers.
Rabies can cause hoarseness, probably due to laryngeal paralysis.
This would be a very unlikely diagnosis in most cases but if there is any chance of exposure to a rabid animal it also has to be considered in the list of possible causes of hoarsenss in a cat. There would also be a possibility of an oral, pharyngeal or nasal foreign body leading to infection or inflammation causing the sneezing and hoarseness. This is not too likely with a long history of problems but it is something else that occasionally causes these problems. It often takes examination under anesthesia to find these, so it is another thing to think about it you and your vet decide on an examination under anesthesia as a necessary diagnostic step. I can not think of a relationship between any of these problems and the soft stools, except that antibiotic use can sometimes cause soft stools or diarrhea.