At the risk of sounding like a quack, and FWIW, raw garlic -- eaten in large amounts -- can possibly help regenerate nerve endings. Many years ago, I lost all feeling on the inside of one of my legs below the knee due to an accident. I had no feeling -- not even pins and needles -- in that area for six months. After reading medical research in an AMA Journal that stated that garlic raises the respiration rate of cells (therefore increasing oxygen in the cells), EVEN IF THEY HAVE NO BLOOD FLOW TO THEM, a bell went off in my head. I had heard before that oxygen regenerates nerve endings. So, I theorized, if I ate a bunch of raw garlic and increased the respiration rate (oxygen content of cells) throughout my body, possibly the damaged nerve endings in my leg would regrow and I would get some feeling back. I ate an entire raw bulb -- not one clove, but an entire bulb -- of raw garlic for 14 days (a very difficult task). After 3 or 4 days of doing this, I began to get sensations of pins and needles in my damaged leg for the first time in half a year. After 10 days, all feeling had returned to my leg. The loss of sensation (or any numbness) never returned.
Many years later, I had a numb sensation on top of one of my collar bones due to the shoulder strap of a heavy backpack bruising the nerve there. I remembered my garlic therapy and ate a bunch of raw garlic for a few days. The numbness went away. Mind you, this second example is of a condition that might have self-corrected anyway. But the leg injury was retractable for 6 months, with absolutely no sign of improvement until I ate the garlic.
In order to make the garlic more easy to eat -- after eating several cloves, the rest of the bulb tended to burn my mouth a bit going down -- I ate it with oily foods such as avocado. The garlic must be eaten raw, to get the full benefits of the volatile oils which seem to be the active ingredient. I also ate only a couple or 3 cloves in one sitting and spread the entire allotment out over the course of each entire day.
I have no idea if the garlic will help your son, especially after 1 year of having his condition. The brain and cranial nerves are very different from peripheral nerves. And I should say that I tried eating a bunch of raw garlic to improve the condition of my vestibular and hearing nerves after discovering I had an AN, and I can't say it helped. That said, I only ate about 4 or 5 cloves a day for the AN-related problems; I couldn't stomach eating an entire bulb. I think it's easier to do something extreme like that when you're younger.
I was hesitant to post this message because it's really such a radical idea, but since you said "any help is so appreciated," I thought it was my duty to tell you of my experience on the off chance that it might help your son. I hope it does.
Best wishes,
Tumbleweed
P.S. I'm not a medical professional, but a paralyzed vocal chord and swallowing difficulties sound more like it could be from a brainstem injury than from damage to cranial nerves, as the brainstem controls the ability to speak and swallow, among other higher functions.