I can really relate to your father's frustration. It can't hurt to try VitaStim therapy which is just electrical stimulation of the swallowing muscles. I had very high hopes for it, but unfortunately it did not work for me.
As to the mucous, I have learned to swish some water around and gargle then spit the mucous out. It took some practice and lots of dribble and spray down the chest and face at first, but it is a great relief to get the mucous out. I even swab my mouth with a tissue to wipe up the especially sticky "glue" like mucous. My oconology dentist made me a palate drop so I can spit better and talk better but nobody has had any success in restoring my ability to swallow.
If his epiglottis is "frozen", there is a chance that it will slowly improve. Unfortunately I don't have any easy answers or remedies for your dad, just empathy.
Charm