first, discuss with your sensei of your issue. i am sure he/she would understand and come up with ways to work around your test. if your sensei doesn't, then leave the dojo.
find someone who you trust to work with you, i.e. be uke for you. might be a female first. just do it slowly, snail speed. get into the position, but don't throw. focus on breathing. count in your head if you need to - breath in for 3 counts, hold for 2, out for 3, hold for 2. do that as many times as you need and gradually increase the speed of your movement to get into the position. again, don't throw. just get into position up to the throwing part. once you comfortable with the first person, find another and another.
another thing that you could also try. stand with your eyes open and focus only on your breathing. have someone you trust walk up to you and touch you. your job is to focus on breathing. their job is to touch you and at slow interval at various locations on your body. when you feel tense, tell that person to back off a bit and you focus on breathing to get back to a relax state. once you back to the relax state, ask your friend to begin again. keep doing in that until they can just walk up to you out of the blue and touch you without you change your breathing pattern. once you can do that, then add another person, then another person, until you have a bunch of people touching you without you changing your breathing pattern. the key is you control the situation of how much and how soon, then transition it to an uncontrol situation at the time of your choosing. it's a systema trick.
I am sure he would work around it for me for testing, but I would personally feel like I wouldn't deserve the belt if I did a work around for the test.
That idea is probably the most terrifying thing I have ever heard. Thank you, because that sounds like exactly what I am looking for.