I sure am sorry you are having the swallowing issues. I want you to know you are Welcome here on Neuro Talk. I am not sure about that particular MRI. Somebody will be along who can identify that particular test. I hope that it can find the cause of your swallowing trouble. I do know it is horrible. I do not have that to the degree you do, but I do choke on food and pills if I am not careful. I have Barretts esophagus which I found out is the reason for it. My medications also dried up my mouth which futher hurts the ability to swallow. I couldn't take the barium test eithor, I got sick.
I hope that when you have this test, that you can relax, and just remember you can get out of the machine, and it is only for a short time. You can listen to music and the valium should help. I have a friend Named John up in Missouri, and he gets that closed in feeling too. I know open MRI's are available, but not in your particular area of the country. Perhaps your doctor allows for that possiblity. I went caving when I was young, and got that closed in feeling and had to get out. I do know that feeling. Just remember it is only for a short time, and that you are safe, and they can hear you if you need any help at all. Even with one that has contrast, or an IV, it isn't so bad if you can just relax. I have had four, and cat scans. All of them can make a person nervous. Most tests do. I don't care much for the dentist, and want to run out the door!
I really hope that this gets to the bottom of the swallowing issue. I know that not having the use of your throat is a terrible burden. We are here for you at Neuro Talk. I hope alot of others will also talk to you. You are in my prayers. ginnie