Another thing I just thought of:
I know that people with hypothyroidism can develop problems swallowing because of an enlarged thyroid gland/goiter. I don't think it would have shown up on the test you took, but it would show up on a thyroid ultrasound. Also, have you ever had your thyroid hormone values looked at? I've been researching many things online, and it also seems that thyroid disease problems can be aggravated if a person has a gluten problem.
I think that it would be worth getting your thyroid checked out. An ultrasound of that area in general sounds like it may be helpful.

Your situation is definitely intriguing to me- I feel like there definitely might be something medical going on- reading the articles I read, I would probably start at the thyroid because hypothyroidism is a fairly common problem.